# Alessio Figalli

Italian mathematician

## Alessio Figalli's AcademicInfluence.com Rankings

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Mathematics

## Alessio Figalli's Degrees

- PhD Mathematics Scuola Normale Superiore di Pisa
- Masters Mathematics Scuola Normale Superiore di Pisa
- Bachelors Mathematics Consorzio ICoN

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## Why Is Alessio Figalli Influential?

(Suggest an Edit or Addition)According to Wikipedia, Alessio Figalli is an Italian mathematician working primarily on calculus of variations and partial differential equations. He was awarded the Peccot-Vimont Prize and the Peccot Lectures in 2012, the EMS Prize in 2012, the Stampacchia Medal in 2015, the Feltrinelli Prize in 2017, and the Fields Medal in 2018. He was an invited speaker at the International Congress of Mathematicians 2014. In 2016 he was awarded a European Research Council grant, and in 2018 he received the Doctorate Honoris Causa from the Université Côte d'Azur. In 2019, he received the Doctorate Honoris Causa from the Polytechnic University of Catalonia.

## Alessio Figalli's Published Works

### Published Works

- A mass transportation approach to quantitative isoperimetric inequalities (2010) (356)
- Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations (2011) (269)
- The power of quantum neural networks (2020) (255)
- Existence and uniqueness of martingale solutions for SDEs with rough or degenerate coefficients (2008) (210)
- Isoperimetry and Stability Properties of Balls with Respect to Nonlocal Energies (2014) (174)
- On the Monge-Ampère equation (2019) (173)
- The Monge-ampere Equation and Its Applications (2017) (171)
- The Monge–Ampère equation and its link to optimal transportation (2013) (148)
- The Optimal Partial Transport Problem (2010) (133)
- Bootstrap regularity for integro-differential operators and its application to nonlocal minimal surfaces (2012) (120)
- Non-local gradient dependent operators (2012) (116)
- Regularity of solutions to the parabolic fractional obstacle problem (2011) (106)
- A refined Brunn-Minkowski inequality for convex sets (2009) (105)
- Nonlocal Tug‐of‐War and the Infinity Fractional Laplacian (2010) (100)
- When is multidimensional screening a convex program? (2009) (99)
- Optimal transportation on non-compact manifolds (2007) (96)
- Mass Transportation on Sub-Riemannian Manifolds (2008) (93)
- Stability for a GNS inequality and the Log-HLS inequality, with application to the critical mass Keller–Segel equation (2011) (82)
- A new transportation distance between non-negative measures, with applications to gradients flows with Dirichlet boundary conditions (2010) (82)
- On the Shape of Liquid Drops and Crystals in the Small Mass Regime (2011) (80)
- On flows associated to Sobolev vector fields in Wiener spaces: an approach \`a la DiPerna-Lions (2008) (78)
- Hölder Continuity and Injectivity of Optimal Maps (2011) (78)
- Regularity and Bernstein-type results for nonlocal minimal surfaces (2013) (75)
- Nearly Round Spheres Look Convex (2012) (74)
- A rigorous derivation from the kinetic Cucker–Smale model to the pressureless Euler system with nonlocal alignment (2017) (72)
- Continuity of optimal transport maps and convexity of injectivity domains on small deformations of 𝕊2 (2009) (68)
- W2,1 regularity for solutions of the Monge–Ampère equation (2013) (68)
- NECESSARY AND SUFFICIENT CONDITIONS FOR CONTINUITY OF OPTIMAL TRANSPORT MAPS ON RIEMANNIAN MANIFOLDS (2011) (67)
- $W^{2,1}$ regularity for solutions of the Monge-Amp\`ere equation (2011) (65)
- Quantitative stability for the Brunn-Minkowski inequality (2014) (63)
- C1 regularity of solutions of the Monge–Ampère equation for optimal transport in dimension two (2009) (63)
- Geodesics in the Space of Measure-Preserving Maps and Plans (2007) (63)
- Transport Maps for $${\beta}$$β-Matrix Models and Universality (2013) (60)
- Strongly Nonlocal Dislocation Dynamics in Crystals (2013) (60)
- Existence of Eulerian Solutions to the Semigeostrophic Equations in Physical Space: The 2-Dimensional Periodic Case (2011) (59)
- Semiclassical limit of quantum dynamics with rough potentials and well‐posedness of transport equations with measure initial data (2010) (59)
- Transport Maps for β-Matrix Models and Universality (2015) (56)
- Sharp stability theorems for the anisotropic Sobolev and log-Sobolev inequalities on functions of bounded variation (2013) (56)
- Partial regularity of brenier solutions of the monge-ampère equation (2010) (55)
- On the Ma–Trudinger–Wang curvature on surfaces (2010) (55)
- Regularity of optimal transport maps on multiple products of spheres (2010) (54)
- A Sharp Stability Result for the Relative Isoperimetric Inequality Inside Convex Cones (2012) (54)
- Sharp boundary behaviour of solutions to semilinear nonlocal elliptic equations (2017) (52)
- Stable solutions to semilinear elliptic equations are smooth up to dimension $9$ (2019) (50)
- On the Hausdorff dimension of the mather quotient (2007) (50)
- Rigidity and sharp stability estimates for hypersurfaces with constant and almost-constant nonlocal mean curvature (2015) (48)
- On the fine structure of the free boundary for the classical obstacle problem (2017) (48)
- Global regularity for the free boundary in the obstacle problem for the fractional Laplacian (2015) (48)
- Regularity results for very degenerate elliptic equations (2014) (47)
- Confinement in nonlocal interaction equations (2012) (47)
- Some New Well-Posedness Results for Continuity and Transport Equations, and Applications to the Chromatography System (2009) (47)
- A global existence result for the semigeostrophic equations in three dimensional convex domains (2012) (46)
- Total Variation Flow and Sign Fast Diffusion in one dimension (2011) (45)
- Regularity Properties of Optimal Maps Between Nonconvex Domains in the Plane (2010) (45)
- A simple proof of the Morse-Sard theorem in Sobolev spaces (2008) (44)
- Sharp global estimates for local and nonlocal porous medium-type equations in bounded domains (2016) (44)
- A General Class of Free Boundary Problems for Fully Nonlinear Elliptic Equations (2012) (44)
- A note on interior W 2 , 1 + ε estimates for the Monge–Ampère equation (2012) (43)
- On the isoperimetric problem for radial log-convex densities (2013) (43)
- Continuity and injectivity of optimal maps for non-negatively cross-curved costs (2009) (43)
- On the regularity of the pressure field of Brenier’s weak solutions to incompressible Euler equations (2008) (43)
- A note on Cheeger sets (2009) (42)
- Existence, Uniqueness, and Regularity of Optimal Transport Maps (2007) (41)
- Geometry of minimizers for the interaction energy with mildly repulsive potentials (2016) (40)
- Absolute continuity of Wasserstein geodesics in the Heisenberg group (2008) (39)
- Local semiconvexity of Kantorovich potentials on non-compact manifolds (2011) (39)
- On the continuity of center-outward distribution and quantile functions (2018) (39)
- Symmetry results for critical anisotropic p-Laplacian equations in convex cones (2019) (39)
- Infinite Speed of Propagation and Regularity of Solutions to the Fractional Porous Medium Equation in General Domains (2015) (38)
- A note on interior $$W^{2,1+ \varepsilon }$$estimates for the Monge–Ampère equation (2012) (38)
- Asymptotics of the $s$-perimeter as $s\searrow 0$ (2012) (36)
- Quantitative stability for sumsets in $R^n$ (2014) (36)
- Universality in several-matrix models via approximate transport maps (2014) (35)
- On stable solutions for boundary reactions: a De Giorgi-type result in dimension 4 + 1 (2017) (34)
- Existence and Uniqueness of Maximal Regular Flows for Non-smooth Vector Fields (2014) (32)
- GRADIENT STABILITY FOR THE SOBOLEV INEQUALITY : THE CASE p ≥ 2 (31)
- Regularity Theory for Local and Nonlocal Minimal Surfaces: An Overview (2017) (31)
- BMO‐Type Norms Related to the Perimeter of Sets (2014) (31)
- Generalized solutions for the Euler equations in one and two dimensions (2009) (30)
- Global Well-posedness of the Spatially Homogeneous Kolmogorov–Vicsek Model as a Gradient Flow (2015) (30)
- High action orbits for Tonelli Lagrangians and superlinear Hamiltonians on compact configuration spaces (2006) (30)
- Semiclassical limit for mixed states with singular and rough potentials (2010) (30)
- An Invitation to Optimal Transport, Wasserstein Distances, and Gradient Flows (2021) (29)
- Free Boundary Regularity in the Parabolic Fractional Obstacle Problem (2016) (29)
- Generic regularity of free boundaries for the obstacle problem (2019) (29)
- Partial regularity for optimal transport maps (2015) (28)
- Sharp gradient stability for the Sobolev inequality (2020) (28)
- GLOBAL-IN-TIME WEAK MEASURE SOLUTIONS, FINITE-TIME AGGREGATION AND CONFINEMENT FOR NONLOCAL INTERACTION EQUATIONS (2009) (25)
- REGULARITY OF OPTIMAL TRANSPORT MAPS (after Ma{Trudinger{Wang and Loeper) (2009) (24)
- Second order stability for the Monge–Ampère equation and strong Sobolev convergence of optimal transport maps (2012) (24)
- Sharp Extinction Rates for Fast Diffusion Equations on Generic Bounded Domains (2019) (24)
- On the Sharp Stability of Critical Points of the Sobolev Inequality (2019) (23)
- Surface measures and convergence of the Ornstein-Uhlenbeck semigroup in Wiener spaces (2010) (23)
- Rigidity and stability of Caffarelli's log-concave perturbation theorem (2016) (22)
- Optimal regularity of the convex envelope (2014) (22)
- Optimal Transport and Curvature (2011) (21)
- On the Lagrangian structure of transport equations: the Vlasov-Poisson system (2014) (21)
- On flows of H3/2-vector fields on the circle (2010) (21)
- A note on the regularity of the free boundaries in the optimal partial transport problem (2009) (20)
- An Approximation Lemma about the Cut Locus, with Applications in Optimal Transport Theory (2008) (18)
- A general class of free boundary problems for fully nonlinear parabolic equations (2015) (18)
- The sharp quantitative Euclidean concentration inequality (2016) (18)
- Regularity of monotone transport maps between unbounded domains (2019) (18)
- Almost everywhere well-posedness of continuity equations with measure initial data (2009) (18)
- Sobolev Regularity for Monge-Ampère Type Equations (2012) (17)
- A variational method for a class of parabolic PDEs (2011) (17)
- Lipschitz Changes of Variables between Perturbations of Log-concave Measures (2015) (16)
- SYNCHRONIZED TRAFFIC PLANS AND STABILITY OF OPTIMA (2008) (16)
- Higher Integrability for Minimizers of the Mumford–Shah Functional (2013) (16)
- Optimal Transportation and Action-Minimizing Measures (2010) (14)
- Convergence to the viscous porous medium equa- tion and propagation of chaos (2008) (14)
- An overview of unconstrained free boundary problems (2015) (14)
- Closing Aubry Sets I (2015) (14)
- On sets of finite perimeter in Wiener spaces: Reduced boundary and convergence to halfspaces (2012) (14)
- A quantitative analysis of metrics on $\mathbf{R}^n$ with almost constant positive scalar curvature, with applications to fast diffusion flows (2016) (13)
- Closing Aubry Sets II (2015) (13)
- Boundary ε-regularity in optimal transportation (2015) (12)
- Free boundary regularity in obstacle problems (2018) (12)
- Gradient stability for the Sobolev inequality: the case $p\geq 2$ (2015) (12)
- A note on the dimension of the singular set in free interface problems (2014) (12)
- REGULARITY OF INTERFACES IN PHASE TRANSITIONS VIA OBSTACLE PROBLEMS - FIELDS MEDAL LECTURE (2018) (11)
- Generic hyperbolicity of Aubry sets on surfaces (2015) (11)
- Stability in geometric and functional inequalities (2014) (11)
- Optimal Regularity for the Convex Envelope and Semiconvex Functions Related to Supersolutions of Fully Nonlinear Elliptic Equations (2019) (11)
- Characterization of isoperimetric sets inside almost-convex cones (2016) (11)
- Quantitative stability of the Brunn-Minkowski inequality for sets of equal volume (2017) (11)
- Strong Sard conjecture and regularity of singular minimizing geodesics for analytic sub-Riemannian structures in dimension 3 (2018) (11)
- Partial $W^{2,p}$ regularity for optimal transport maps (2012) (11)
- Tangent cut loci on surfaces (2011) (11)
- The monge problem on non-compact manifolds (2007) (11)
- WKB Analysis of Bohmian Dynamics (2012) (11)
- A scale-dependent notion of effective dimension (2020) (11)
- A quantitative analysis of metrics on $\R^n$ with almost constant positive scalar curvature, with applications to Yamabe and fast diffusion flows (2016) (10)
- Weak KAM theory for a weakly coupled system of Hamilton–Jacobi equations (2016) (9)
- How to recognize convexity of a set from its marginals (2013) (9)
- Strong Stability for the Wulff Inequality with a Crystalline Norm (2019) (9)
- Nonlocal and Nonlinear Diffusions and Interactions: New Methods and Directions - Cetraro, Italy (2017) (9)
- A sharp Freiman type estimate for semisums in two and three dimensional Euclidean spaces (2019) (9)
- Effective dimension of machine learning models (2021) (8)
- On supporting hyperplanes to convex bodies (2011) (8)
- On the regularity of the free boundary in the p-Laplacian obstacle problem ☆ (2017) (8)
- Strong displacement convexity on Riemannian manifolds (2007) (8)
- The singular set in the Stefan problem (2021) (8)
- Symplectic $G$-capacities and integrable systems (2015) (8)
- Nonlinear bounds in Hölder spaces for the Monge–Ampère equation (2015) (7)
- Perimeter of sets and BMO-type norms (2014) (7)
- Isoperimetric-type inequalities on constant curvature manifolds (2012) (6)
- Global Existence for the Semigeostrophic Equations via Sobolev Estimates for Monge-Ampère (2018) (6)
- Aubry sets , Hamilton-Jacobi equations , and the Mañé Conjecture (2013) (6)
- QUANTITATIVE ISOPERIMETRIC INEQUALITIES , WITH APPLICATIONS TO THE STABILITY OF LIQUID DROPS AND CRYSTALS (2010) (6)
- Stability results for the brunn-minkowski inequality (2015) (6)
- Quantitative stability results for the Brunn-Minkowski inequality (2014) (6)
- STABILITY FOR THE SOBOLEV INEQUALITY WITH EXPLICIT CONSTANTS (2022) (5)
- REGULARITY OF CODIMENSION-1 MINIMIZING CURRENTS UNDER MINIMAL ASSUMPTIONS ON THE INTEGRAND (2016) (5)
- Continuity of ball packing density on moduli spaces of toric manifolds (2014) (5)
- Existence and Uniqueness Results for the Continuity Equation and Applications to the Chromatography System (2011) (5)
- A geometric approach to correlation inequalities in the plane (2014) (4)
- Sobolev Regularity for the Monge−Ampère Equation, With Application to the Semigeostrophic Equations (2014) (4)
- Optimal Regularity and Structure of the Free Boundary for Minimizers in Cohesive Zone Models (2017) (4)
- REGULARITY OF OPTIMAL TRANSPORT MAPS [ after Ma – (2009) (4)
- Partial Regularity Results in Optimal Transportation (2014) (4)
- On the Convexity of Injectivity Domains on Nonfocal Manifolds (2014) (4)
- Complete classification of global solutions to the obstacle problem (2022) (4)
- Sharp stability for Sobolev and log-Sobolev inequalities, with optimal dimensional dependence (2022) (4)
- Stability results on the smoothness of optimal transport maps with general costs (2016) (4)
- 1 Variational models for the incompressible Euler equations (2014) (3)
- Hölder Continuity and Injectivity of Optimal Maps (2013) (3)
- Invariant measures of Hamiltonian systems with prescribed asymptotic Maslov index (2007) (3)
- Fine properties of minimizers of mechanical Lagrangians with Sobolev potentials (2011) (3)
- Regularity of $\textrm{codimension-}1$ minimizing currents under minimal assumptions on the integrand (2017) (2)
- On the density function on moduli spaces of toric 4-manifolds (2014) (2)
- An Obstacle Problem for Conical Deformations of Thin Elastic Sheets (2017) (2)
- On the Monge-Amp\`ere equation (2018) (2)
- On stable solutions for boundary reactions: a De Giorgi-type result in dimension 4 + 1 (2019) (2)
- A geometric lower bound on Grad's number (2009) (2)
- Strategic Execution Trajectories (2021) (1)
- Boundary $\varepsilon$-regularity in optimal transportation (2014) (1)
- Stability in geometric & functional inequalities (2012) (1)
- Stability of the gagliardo-nirenberg sobolev inequality (2016) (1)
- Optimal Regularity and Structure of the Free Boundary for Minimizers in Cohesive Zone Models (2020) (1)
- Lipschitz regularity in vectorial linear transmission problems (2020) (1)
- Regularity properties of monotone measure-preserving maps (2023) (1)
- Uniform boundedness for finite Morse index solutions to supercritical semilinear elliptic equations (2021) (1)
- Quantitative stability for sumsets in R[superscript n] (2015) (1)
- Partial Differential Equations and Geometric Measure Theory: Cetraro, Italy 2014 (2018) (1)
- Global C 1 ,α Regularity for Monge–Ampère Equation and Convex Envelope (2022) (1)
- Weak KAM theory for a weakly coupled system of Hamilton–Jacobi equations (2016) (1)
- Generic regularity of free boundaries for the obstacle problem (2020) (0)
- Infinite-width limit of deep linear neural networks (2022) (0)
- 2 Lax-Oleinik semigroup and Weak KAM Theorem (2012) (0)
- Sharp boundary behaviour of solutions to semilinear nonlocal elliptic equations (2018) (0)
- Variational models for incompressible Euler equations and measures concentrated on action-minimizing paths (2007) (0)
- Quantitative stability of the Brunn-Minkowski inequality for sets of equal volume (2017) (0)
- Existence and Uniqueness of Maximal Regular Flows for Non-smooth Vector Fields (2015) (0)
- Global Well-posedness of the Spatially Homogeneous Kolmogorov–Vicsek Model as a Gradient Flow (2017) (0)
- A transportation approach to universality in random matrix theory (2017) (0)
- Free boundary regularity in the Stefan problem (2021) (0)
- W2,1 regularity for solutions of the Monge–Ampère equation (2012) (0)
- On the Sharp Stability of Critical Points of the Sobolev Inequality (2020) (0)
- A quantitative stability result for the Pr\'ekopa-Leindler inequality for arbitrary measurable functions (2022) (0)
- A transportation approach to universality in random matrix theory (2016) (0)
- Programme on “ Optimal Transport ” April 15 – June 14 , 2019 organized (2019) (0)
- A GENERAL CLASS OF UNCONSTRAINED FREE BOUNDARIES (2015) (0)
- Ip0 the Siag/analysis of Partial Differential Equa- Tions Prize Lecture: Weak Solutions of the Euler Equations: Non-uniqueness and Dissipation Ip1 Coupling between Internal and Surface Waves in a Two-layers Fluid (0)
- Isoperimetry and Stability Properties of Balls with Respect to Nonlocal Energies (2014) (0)
- Sujet: Optimal transport, Euler equations, (2009) (0)
- Generic hyperbolicity of Aubry sets on surfaces (2014) (0)
- On the prescribed negative Gauss curvature problem for graphs (2022) (0)
- Optimal Regularity for the Convex Envelope and Semiconvex Functions Related to Supersolutions of Fully Nonlinear Elliptic Equations (2019) (0)
- NONLOCAL DISLOCATION DYNAMICS IN CRYSTALS (2014) (0)
- 2 The optimal transport problem (2010) (0)
- A Sharp Stability Result for the Relative Isoperimetric Inequality Inside Convex Cones (2011) (0)
- On the fine structure of the free boundary for the classical obstacle problem (2018) (0)
- Optimal Transportation and Differential Geometry (2012) (0)
- Lecture notes on variational models for incompressible Euler equations (2010) (0)
- M G ] 2 4 D ec 2 01 4 Quantitative stability for the Brunn-Minkowski inequality (2014) (0)
- Corrigendum: Semiclassical Limit of Quantum Dynamics with Rough Potentials and Well‐Posedness of Transport Equations with Measure Initial Data (2013) (0)
- ON INTERIOR C-ESTIMATES FOR THE MONGE-AMPÈRE EQUATION (2017) (0)
- Calculus of Variations (2019) (0)
- PR ] 7 J ul 2 01 4 TRANSPORT MAPS FOR β-MATRIX MODELS AND UNIVERSALITY (2014) (0)
- A general class of free boundary problems for fully nonlinear parabolic equations (2014) (0)
- Book Review: Optimal transport: old and new (2010) (0)
- Partial regularity for optimal transport maps (2014) (0)
- On the isoperimetric problem for radial log-convex densities (2012) (0)
- An Obstacle Problem for Conical Deformations of Thin Elastic Sheets (2017) (0)
- Sobolev Regularity for the Monge−Ampère Equation, With Application to the Semigeostrophic Equations (2014) (0)
- On the obstacle problem for the 1D wave equation (2019) (0)
- Higher Integrability for Minimizers of the Mumford–Shah Functional (2014) (0)
- A quantitative analysis of metrics with almost constant scalar curvature on the sphere (2016) (0)
- A General Class of Free Boundary Problems for Fully Nonlinear Elliptic Equations (2014) (0)
- Synchronized tra c plans and stability of optima (2007) (0)

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