Andrea Malchiodi | Academic Influence

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Andrea Malchiodi

Mathematics

#2822

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#4278

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Differential Geometry

#94

World Rank

#111

Historical Rank

Geometry

#109

World Rank

#167

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Measure Theory

#2982

World Rank

#3542

Historical Rank

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Mathematics

Andrea Malchiodi's Degrees

PhD Mathematics University of Pavia
Masters Mathematics University of Pavia
Bachelors Mathematics University of Pavia

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Why Is Andrea Malchiodi Influential?

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According to Wikipedia, Andrea Malchiodi is an Italian mathematician who is active in the fields of partial differential equations and calculus of variations, with several contributions to geometric analysis. Scientific activity Malchiodi received his Ph.D. in mathematics from the International School for Advanced Studies in 2000 under the supervision of Antonio Ambrosetti. He is a professor of mathematics at the Scuola Normale Superiore at Pisa. He was previously professor of mathematics at the International School for Advanced Studies and at the University of Warwick. Malchiodi has developed topological and analytical methods allowing to deal with a number of questions in geometric analysis, such as the Yamabe problem, the scalar curvature problem, problems coming from fourth order conformal geometry and concentration for singular perturbation problems. In particular, he proved some new intricate forms of improved Moser-Trudinger inequalities allowing to prove existence results for singular Liouville equations. Similar types of inequalities allow to prove existence results for Toda systems on surfaces. Malchiodi has been visiting professor in many universities and institutions, amongst which are Stanford University, The Institute for Advanced Study at Princeton, and ETH at Zurich. He belongs to the editorial board of several mathematical journals and is one of the managing editors of the journal Calculus of Variations & PDE.

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Andrea Malchiodi's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Perturbation Methods and Semilinear Elliptic Problems on R^n (2005) (325)
Nonlinear Analysis and Semilinear Elliptic Problems (2007) (296)
Ground states of nonlinear Schrödinger equations with potentials vanishing at infinity (2005) (267)
Multiplicity Results for some Nonlinear¶Schrödinger Equations with Potentials (2000) (261)
Existence of conformal metrics with constant Q-curvature (2004) (242)
Singularly Perturbed Elliptic Equations with Symmetry: Existence of Solutions Concentrating on Spheres, Part I (2003) (221)
Boundary concentration phenomena for a singularly perturbed elliptic problem (2002) (163)
Singularly perturbed elliptic equations with symmetry: Existence of solutions concentrating on spheres, part II (2004) (151)
Minimal surfaces in pseudohermitian geometry (2004) (143)
Nonlinear Analysis and Semilinear Elliptic Problems: Contents (2007) (124)
Multidimensional boundary layers for a singularly perturbed Neumann problem (2004) (119)
Bound states of nonlinear Schrödinger equations with potentials vanishing at infinity (2006) (106)
Morse theory and a scalar field equation on compact surfaces (2008) (106)
Supercritical conformal metrics on surfaces with conical singularities (2011) (106)
PRESCRIBING A FOURTH ORDER CONFORMAL INVARIANT ON THE STANDARD SPHERE — PART I: A PERTURBATION RESULT (2001) (96)
Concentration at curves for a singularly perturbed Neumann problem in three-dimensional domains (2005) (87)
Q-curvature flow on S^4 (2006) (80)
Compactness of solutions to some geometric fourth-order equations (2004) (79)
New Improved Moser–Trudinger Inequalities and Singular Liouville Equations on Compact Surfaces (2010) (74)
Topological methods for an elliptic equation with exponential nonlinearities (2008) (74)
Concentration on minimal submanifolds for a singularly perturbed Neumann problem (2006) (73)
A general existence result for the Toda system on compact surfaces (2013) (70)
Multiple clustered layer solutions for semilinear Neumann problems on a ball (2005) (69)
A strong maximum principle for the Paneitz operator and a non-local flow for the $Q$-curvature (2014) (68)
On the Yamabe problem and the scalar curvature problems under boundary conditions (2002) (68)
A Variational Analysis of the Toda System on Compact Surfaces (2011) (62)
Some existence results for the Toda system on closed surfaces (2007) (62)
Weighted barycentric sets and singular Liouville equations on compact surfaces (2011) (61)
A MULTIPLICITY RESULT FOR THE YAMABE PROBLEM ON SN (1999) (57)
A perturbation result for the Webster scalar curvature problem on the CR sphere (2002) (57)
Critical points of the Moser-Trudinger functional on a disk (2012) (56)
Some new entire solutions of semilinear elliptic equations on Rn (2009) (55)
An Improved Geometric Inequality via Vanishing Moments, with Applications to Singular Liouville Equations (2012) (52)
Prescribing scalar and boundary mean curvature on the three dimensional half sphere (2003) (52)
Non-compactness and multiplicity results for the Yamabe problem on Sn (2001) (46)
Nonlinear Analysis and Semilinear Elliptic Problems: Preface (2007) (45)
The prescribed boundary mean curvature problem on B4 (2004) (44)
A Positive Mass Theorem in Three Dimensional Cauchy–Riemann Geometry (2013) (42)
Prescribing a fourth order conformal invariant on the standard sphere, Part II: blow-up analysis and applications (2001) (40)
A Codazzi-like equation and the singular set for C1 smooth surfaces in the Heisenberg group (2010) (35)
Concentration phenomena for nonlinear Schrödinger equations: Recent results and new perspectives (2007) (32)
A topological join construction and the Toda system on compact surfaces of arbitrary genus (2015) (30)
Boundary interface for the Allen–Cahn equation (2007) (30)
Solutions to the nonlinear Schrödinger equation carrying momentum along a curve (2009) (29)
On the Symmetric Scalar Curvature Problem on Sn (2001) (29)
SOME REMARKS ON THE EQUATION FOR VARYING λ, p AND VARYING DOMAINS* (2002) (29)
The scalar curvature problem on $S^n$: an approach via Morse theory (2002) (28)
Conformal Metrics with Constant Q-Curvature (2007) (28)
Boundary-clustered interfaces for the Allen–Cahn equation (2007) (27)
Transition layer for the heterogeneous Allen–Cahn equation (2007) (24)
Solutions concentrating at curves for some singularly perturbed elliptic problems (2004) (24)
A Moser-Trudinger inequality for the singular Toda system (2013) (23)
Existence and non-existence results for the SU(3) singular Toda system on compact surfaces (2015) (23)
Prescribing Morse Scalar Curvatures: Pinching and Morse Theory (2019) (21)
SINGULAR ELLIPTIC PROBLEMS WITH CRITICAL GROWTH (2002) (20)
Minimal surfaces in pseudohermitian geometry and the Bernstein problem in the Heisenberg group (2004) (20)
Axial symmetry of some steady state solutions to nonlinear Schrödinger equations (2011) (19)
On the Leray-Schauder degree of the Toda system on compact surfaces (2013) (18)
A fourth order uniformization theorem on some four manifolds with large total Q-curvature (2005) (18)
Solutions, concentrating on spheres, to symmetric singularly perturbed problems (2002) (18)
Prescribing Morse Scalar Curvatures: Blow-Up Analysis (2018) (17)
Perturbation methods and semilinear elliptic problems on R[superscript n] (2006) (17)
Concentration of solutions for some singularly perturbed mixed problems : asymptotics of minimal energy solutions (2010) (17)
Conformal metrics with prescribed gaussian and geodesic curvatures (2018) (16)
Adiabatic limits of closed orbits for some Newtonian systems in R-n (2000) (14)
Some remarks on the equation u = (1 + u) p for varying , p and varying domains (2001) (14)
Concentration of Solutions for Some Singularly Perturbed Mixed Problems: Existence Results (2010) (14)
Prescribing Morse scalar curvatures: Subcritical blowing-up solutions (2018) (14)
Curvature theory of boundary phases: the two-dimensional case (2002) (13)
Asymptotic Morse Theory for the Equation ∆ v = 2 vx ∧ vy (2004) (13)
Asymptotic Morse Theory for the Delta-V Equation (2005) (13)
A class of existence results for the singular Liouville equation (2011) (11)
Concentration at manifolds of arbitrary dimension for a singularly perturbed Neumann problem (2006) (11)
Symmetry properties of some solutions to some semilinear elliptic equations (2014) (11)
Embedded area‐constrained Willmore tori of small area in Riemannian three‐manifolds I: minimization (2014) (9)
Geometric analysis and PDEs (2009) (8)
Critical metrics for Log-determinant functionals in conformal geometry (2019) (8)
Scalar curvature under boundary conditions (2000) (8)
Multiple positive solutions of some elliptic equations in R N (2001) (7)
Existence results for a super-Liouville equation on compact surfaces (2019) (7)
Foliation by Area-constrained Willmore Spheres Near a Nondegenerate Critical Point of the Scalar Curvature (2018) (7)
Concentration of Solutions for Some Singularly Perturbed Neumann Problems (2009) (6)
Ground state Dirac bubbles and Killing spinors (2020) (6)
Non-uniqueness Results for Critical Metrics of Regularized Determinants in Four Dimensions (2011) (6)
Embedded area-constrained Willmore tori of small area in Riemannian three-manifolds, II: Morse Theory (2014) (6)
Conformal metrics with prescribed scalar and mean curvature (2021) (5)
Construction of multidimensional spike-layers (2005) (5)
Variational analysis of Toda systems (2017) (5)
Boundedness of Palais-Smale sequences associated to a fourth-order equation in conformal geometry (2004) (5)
A Note on the Critical Laplace Equation and Ricci Curvature (2022) (4)
LIMITS OF α-HARMONIC MAPS (2018) (4)
A variational approach to Liouville equations (2017) (4)
A note on the scalar curvature problem in the presence of symmetries (2000) (4)
Prescribing Morse Scalar Curvatures (2022) (4)
Variational methods for singular Liouville equations (2010) (3)
Solutions to the nonlinear Schroedinger equation carrying momentum along a curve. Part I: study of the limit set and approximate solutions (2007) (3)
Existence Results for Super-Liouville Equations on the Sphere via Bifurcation Theory (2020) (3)
On Singular Liouville Equations and Systems (2017) (3)
Critical points of the Moser–Trudinger functional on closed surfaces (2020) (3)
Periodic Solutions to a Cahn–Hilliard–Willmore Equation in the Plane (2017) (3)
Variational theory for Liouville equations with singularities (2009) (3)
A gap theorem for α-harmonic maps between two-spheres (2019) (3)
Limits of $\alpha$-harmonic maps (2015) (3)
On the Sobolev quotient of three-dimensional CR manifolds (2019) (3)
Some existence results for the scalar curvature problem via Morse theory (1999) (3)
Area-constrained Willmore surfaces of small area in Riemannian three-manifolds: an approach via Lyapunov-Schmidt reduction (Regularity and Singularity for Partial Differential Equations with Conservation Laws) (2017) (3)
Entire solutions of autonomous equations on Rn with nontrivial asymptotics (2008) (3)
Partial Differential Equations — New classes of entire solutions for semilinear elliptic problems in ℝn (2010) (3)
Solutions to the nonlinear Schroedinger equation carrying momentum along a curve. Part II: proof of the existence result (2007) (2)
Min–max schemes for SU(3) Toda systems (2017) (2)
Asymptotic Morse theory for the equation $\D v = 2 v_x \wedge v_y$ (2002) (2)
Nonlinear Analysis and Semilinear Elliptic Problems: Saddle points and min-max methods (2007) (2)
Existence and multiplicity results for some problems in Riemannian geometry (2000) (2)
Concentrating solutions of some singularly perturbed elliptic equations (2008) (2)
Nonlinear Analysis and Semilinear Elliptic Problems: Morse theory (2007) (1)
On some variational problems involving capacity, torsional rigidity, perimeter and measure (2021) (1)
Min-max solutions for super sinh-Gordon equations on compact surfaces (2021) (1)
Asymptotic Morse theory for the equation $\Delta v=2v\sb x\wedge v\sb y$ (2005) (1)
Mean field equations and domains of first kind (2020) (1)
Double bubbles with high constant mean curvatures in Riemannian manifolds (2021) (1)
Nonlinear Analysis and Semilinear Elliptic Problems: Bifurcation for problems on ℝ n (2007) (1)
Uniformizing Surfaces with Conical Singularities (2015) (1)
Asymptotic Morse Theory for the Equation Deltav = 2v~x ¿ v~y (2005) (1)
Perturbative techniques in conformal geometry (2022) (1)
{\L}ojasiewicz inequalities near simple bubble trees (2020) (1)
ISOPERIMETRIC DOMAINS IN HOMOGENEOUS THREE-MANIFOLDS AND THE ISOPERIMETRIC CONSTANT OF THE HEISENBERG GROUP H (2015) (1)
Isoperimetric domains in homogeneous three-manifolds and the isoperimetric constant of the Heisenberg group $\mathsf{H}^1$ (2015) (1)
Some remarks on the equation $-Delta u=lambda(1+u)^p$ for varying $lambda$, $p$ and varying domains (2002) (1)
On Conformal Metrics with Constant $Q$-Curvature (2019) (1)
Existence and multiplicity of solutions for problems in Geometrical Analysis (2010) (1)
A pr 2 00 1 Prescribing a fourth order conformal invariant on the standard sphere , Part II : blow up analysis and applications (2001) (1)
Prescribing scalar and boundary mean curvature on the three dimensional sphere (2002) (1)
Nonlinear Analysis and Semilinear Elliptic Problems: Topological degree, I (2007) (0)
Nonlinear Analysis and Semilinear Elliptic Problems: Topological degree, II: global properties (2007) (0)
A P ] 1 A ug 2 00 7 Solutions to the nonlinear Schrödinger equation carrying momentum along a curve . Part II : proof of the existence result (2007) (0)
Multiple positive solutions of some elliptic equations in \bold R\sp N (2001) (0)
On critical points of the relative fractional perimeter (2018) (0)
Variational analysis for singular Liouville equations (2012) (0)
Convex properties of positive solutions for a class of quasi-linear elliptic problems (2020) (0)
A P ] 1 2 A pr 2 00 1 Prescribing a fourth order conformal invariant on the standard sphere , Part II : blow up analysis and applications (2001) (0)
Lioville Equations and Functional Determinants (2018) (0)
Some recent results about a class of singularly perturbed elliptic equations (2008) (0)
Variational analysis of Toda systems (2017) (0)
Geometric Analysis and PDEs: Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 11-16, 2007 (2009) (0)
The functional determinant of the Paneitz operator (2011) (0)
Preliminary Schedule of Invited Talks August 9th, 2010 8:40-8:50 Welcome to the workshop and the BIRS centre 8:50-9:30 Prof. D. Jerison (MIT) Title: A gradient bound for free boundaries (2010) (0)
Periodic solutions to the Cahn-Hilliard equation in the plane (2017) (0)
Nonlinear Analysis and Semilinear Elliptic Problems: A primer on bifurcation theory (2007) (0)
Nonlinear Analysis and Semilinear Elliptic Problems: Critical points of even functionals on symmetric manifolds (2007) (0)
Nonlinear Analysis and Semilinear Elliptic Problems: Some problems arising in differential geometry (2007) (0)
Non-uniqueness Results for Critical Metrics of Regularized Determinants in Four Dimensions (2012) (0)
Nonlinear Analysis and Semilinear Elliptic Problems: Perturbation methods (2007) (0)
Nonlinear Analysis and Semilinear Elliptic Problems: Constrained critical points (2007) (0)
Poster 148: Acute Paraplegia After an Intrathecal Baclofen Trial for Spasticity Management: A Case Report (2005) (0)
Anniversary (2012) (0)
Sharp bounds on the Nusselt number in Rayleigh-Bénard convection (2020) (0)
Critical points of arbitrary energy for the Trudinger-Moser embedding in planar domains (2022) (0)
Abstracts 8 apr 2019 (2019) (0)
Existence and regularity for prescribed Lorentzian mean curvature hypersurfaces, and the Born-Infeld model (2021) (0)
Nonlinear Analysis and Semilinear Elliptic Problems: Vortex rings in an ideal fluid (2007) (0)
0 M ay 2 00 2 Asymptotic Morse theory for the equation ∆ v = 2 v x ∧ v y (2008) (0)
A variational approach to Liouville equations (2016) (0)
An Improved Geometric Inequality via Vanishing Moments, with Applications to Singular Liouville Equations (2013) (0)
On the scalar curvature problem under symmetry (1999) (0)
Nonlinear Analysis and Semilinear Elliptic Problems: Critical points: extrema (2007) (0)
Nonlinear Analysis and Semilinear Elliptic Problems: Lusternik–Schnirelman theory (2007) (0)
Critical points of the Moser-Trudinger functional (2011) (0)
Min–max schemes for SU(3) Toda systems (2016) (0)
Nonlinear Analysis and Semilinear Elliptic Problems: Preliminaries (2007) (0)
Nonlinear Analysis and Semilinear Elliptic Problems: Further results on elliptic Dirichlet problems (2007) (0)
Mathematical Analysis — Variational methods for singular Liouville equations (2010) (0)
Recent progress on the Yamabe problem (2012) (0)
On a class of nonlinear equations with exponential nonlinearities and measure data (2010) (0)
Nonlinear Analysis and Semilinear Elliptic Problems: Deformations and the Palais–Smale condition (2007) (0)
Nonlinear Analysis and Semilinear Elliptic Problems: The concentration compactness principle (2007) (0)
Nonlinear Analysis and Semilinear Elliptic Problems: References (2007) (0)
Periodic Solutions to a Cahn–Hilliard–Willmore Equation in the Plane (2017) (0)
Asymptotic morse theory for the equation Δv = 2vxv y (2005) (0)
Solvability and regularity for the electrostatic Born-Infeld equation with general charges (2021) (0)
Nonlinear Analysis and Semilinear Elliptic Problems: Qualitative results (2007) (0)
Perturbative techniques for the construction of spike-layers (2020) (0)

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