Tristan Rivière
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French mathematician
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Differential Geometry
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Measure Theory
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Mathematics
Why Is Tristan Rivière Influential?
(Suggest an Edit or Addition)According to Wikipedia, Tristan Rivière is a French mathematician, working on partial differential equations and the calculus of variations. Biography Rivière studied at the École Polytechnique and obtained his PhD in 1993 at the Pierre and Marie Curie University, under the supervision of Fabrice Bethuel, with a thesis on harmonic maps between manifolds. In 1992 he was appointed chargé de recherche at CNRS. In 1997 he received his habilitation at the University of Paris-Sud in Orsay. From 1999 to 2000 he was a visiting associate professor at the Courant Institute of Mathematical Sciences . Since 2003 he is full professor at ETH Zurich and since 2009 he is the Director of the Institute for Mathematical Research at ETH.
Tristan Rivière'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
- Conservation laws for conformally invariant variational problems (2006) (238)
- Analysis aspects of Willmore surfaces (2008) (184)
- Linear and Nonlinear Aspects of Vortices (2000) (133)
- Vortices for a variational problem related to superconductivity (1995) (123)
- Complex Ginzburg-Landau equations in high dimensions and codimension two area minimizing currents (1999) (112)
- Quantization effects for −Δu = u(1 − |u|2) in ℝ2 (1994) (109)
- Three-term commutator estimates and the regularity of $\half$-harmonic maps into spheres (2011) (93)
- Sub-criticality of non-local Schrödinger systems with antisymmetric potentials and applications to half-harmonic maps (2010) (92)
- Variational Principles for immersed Surfaces with $L^2$-bounded Second Fundamental Form (2010) (91)
- Line vortices in the U(1) Higgs model (1996) (90)
- Néel and Cross-Tie Wall Energies for Planar Micromagnetic Configurations (2002) (86)
- Conservation Laws for Fourth Order Systems in Four Dimensions (2006) (86)
- A quantization property for static Ginzburg-Landau vortices (2001) (77)
- Everywhere discontinuous harmonic maps into spheres (1995) (72)
- Linear and Nonlinear Aspects of Vortices: The Ginzburg-andau Model (2000) (68)
- Partial regularity for harmonic maps and related problems (2006) (67)
- Weak density of smooth maps for the Dirichlet energy between manifolds (2003) (66)
- A partial regularity result for a class of Stationary Yang-Mills Fields in high dimension (2003) (64)
- Energy quantization for Willmore surfaces and applications (2011) (64)
- Compactness, Kinetic Formulation, and Entropies for a Problem Related to Micromagnetics (2003) (63)
- Vortex energy and vortex bending for a rotating Bose-Einstein condensate (2001) (63)
- Energy quantization for harmonic maps (2002) (62)
- Connecting topological Hopf singularities (2003) (54)
- Blow-up analysis of a nonlocal Liouville-type equation (2015) (52)
- Resolutions of the prescribed volume form equation (1996) (48)
- Lipschitz conformal immersions from degenerating Riemann surfaces with L2-bounded second fundamental forms (2013) (46)
- Dense Subsets of H1/2(S2, S1) (2000) (44)
- Willmore spheres in compact Riemannian manifolds (2012) (44)
- The singular set of 1-1 integral currents (2003) (43)
- Embedded Surfaces of Arbitrary Genus Minimizing the Willmore Energy Under Isoperimetric Constraint (2013) (38)
- Conformally Invariant Variational Problems (2012) (36)
- Interpolation spaces and energy quantization for Yang–Mills fields (2002) (34)
- The singular set of J-holomorphic maps into projective algebraic varieties (2004) (34)
- A Quantization Property for Moving Line Vortices (2001) (33)
- A viscosity method in the min-max theory of minimal surfaces (2015) (33)
- Angular Energy Quantization for Linear Elliptic Systems with Antisymmetric Potentials and Applications (2011) (33)
- A Sharp Nonlinear Gagliardo–Nirenberg-Type Estimate and Applications to the Regularity of Elliptic Systems (2005) (32)
- The rectifiability of entropy measures in one space dimension (2003) (30)
- Minimizing fibrations and $p$-harmonic maps in homotopy classes from $S^3$ into $S^2$ (1998) (30)
- SINGULARITY REMOVABILITY AT BRANCH POINTS FOR WILLMORE SURFACES (2013) (30)
- 3-Commutators Estimates and the Regularity of 1/2-Harmonic Maps into Spheres (2009) (26)
- Immersed spheres of finite total curvature into manifolds (2013) (24)
- Energy quantization for biharmonic maps (2011) (23)
- On the rectifiability of defect measures arising in a micromagnetics model (2002) (22)
- The regularity of Special Legendrian Integral Cycles (2009) (22)
- Connecting rational homotopy type singularities (2008) (20)
- Weak immersions of surfaces with ²-bounded second fundamental form (2016) (20)
- Uniqueness of tangent cones for semicalibrated integral $2$-cycles (2005) (20)
- Local Palais-Smale Sequences for the Willmore Functional (2009) (20)
- Asymptotic analysis for the Ginzburg-Landau equations (1999) (19)
- A viscosity property of minimizing micromagnetic configurations (2003) (18)
- The resolution of the Yang-Mills Plateau problem in super-critical dimensions (2013) (18)
- A Viscosity Method for the Min-Max Construction of Closed Geodesics (2015) (16)
- Willmore minmax surfaces and the cost of the sphere eversion (2015) (16)
- The Ginzburg-Landau Equation in ℂ (2000) (16)
- A lower‐epiperimetric inequality for area‐minimizing surfaces (2004) (15)
- A proof of the multiplicity 1 conjecture for min-max minimal surfaces in arbitrary codimension (2018) (15)
- Weak immersions of surfaces with L 2-bounded second fundamental form Lecture 1 PCMI Graduate Summer School 2013 (2013) (15)
- Optimal estimate for the gradient of Green functions on degenerating surfaces and applications (2013) (15)
- The Classification of Branched Willmore Spheres in the 3-Sphere and the 4-Sphere (2017) (15)
- A Resolution of the Poisson Problem for Elastic Plates (2018) (15)
- Towards Jaffe and Taubes Conjectures in the strongly repulsive limit (2002) (14)
- Sub-criticality of Schrödinger systems with antisymmetric potentials (2009) (14)
- High-dimensional helicities and rigidity of linked foliations (2002) (13)
- Critical weak immersed Surfaces within Sub-manifolds of the Teichm\"uller Space (2013) (12)
- Ginzburg-Landau vortices : the static model (2000) (12)
- Sequences of Smooth Global Isothermic Immersions (2012) (12)
- Weak Closure of Singular Abelian Lp-Bundles in 3 Dimensions (2010) (11)
- Energy quantization of Willmore surfaces at the boundary of the moduli space (2016) (11)
- Regularity for micromagnetic configurations having zero jump energy (2002) (10)
- Integrability by Compensation in the Analysis of Conformally Invariant Problems (2009) (10)
- The regularity of conformal target harmonic maps (2016) (9)
- Asymptotic Analysis of Branched Willmore Surfaces (2011) (9)
- The Variations of Yang–Mills Lagrangian (2015) (8)
- UNE RESOLUTION DE L'EQUATION A FORME VOLUME PRESCRITE (1994) (8)
- A frame energy for immersed tori and applications to regular homotopy classes (2013) (8)
- Global gauges and global extensions in optimal spaces (2013) (7)
- Lower Semi-continuity of the Index in the Viscosity Method for Minimal Surfaces (2018) (7)
- The Regularity of Parametrized Integer Stationary Varifolds in Two Dimensions (2017) (7)
- Classification of branched Willmore spheres in $S^3$ and $S^4$ (2017) (6)
- Concentration estimates for entropy measures (2003) (6)
- Bubbling and Regularity Issues in Geometric Non-linear Analysis (2003) (6)
- Uniform regularity results for critical and subcritical surface energies (2017) (6)
- Minmax Hierarchies and Minimal Surfaces in Manifolds (2017) (5)
- A Pohozaev-type formula and Quantization of Horizontal Half-Harmonic Maps (2016) (5)
- A Remark on the Use of Differential Forms for the Skyrme Problem (1998) (5)
- Approximating J-holomorphic curves by holomorphic ones (2004) (5)
- Limiting Domain Wall Energy in Micromagnetism (2000) (5)
- Bourbaki Seminar 1081 : Min-max methods and the Willmore conjecture, after Fernando Codá Marques and André Arroja Neves (2014) (5)
- The parametric approach to the Willmore flow (2020) (4)
- Uniqueness of tangent cones for calibrated 2-cycles (2005) (4)
- Horizontal $\alpha$-Harmonic Maps (2016) (4)
- The role of conservation laws in the analysis of conformally invariant problems (2012) (4)
- Minmax Hierarchies, Minimal Fibrations and a PDE based Proof of the Willmore Conjecture (2020) (4)
- ASYMPTOTIC ANALYSIS OF MINIMIZING HARMONIC MAPS OF REGIONS BOUNDED BY TWO CIRCLES (1991) (3)
- Higher Regularity of Weak Limits of Willmore Immersions I (2019) (3)
- The regularity of parametrized integer 2-rectifiable stationary varifolds (2017) (3)
- A Minimality Property for Entropic Solutions to Scalar Conservation Laws in 1 + 1 Dimensions (2009) (3)
- Ends of immersed minimal and Willmore surfaces in asymptotically flat spaces (2015) (3)
- Bergman-Bourgain-Brezis-type Inequality (2020) (2)
- The Space of Weak Connections in High Dimensions (2018) (2)
- Tori in $$S^3$$S3 Minimizing Locally the Conformal Volume (2014) (2)
- Exploring the unknown: The work of Louis Nirenberg on partial differential equations (2015) (2)
- Bubbling Phenomena and Weak Convergence for Maps in W (2005) (2)
- Sobolev Critical Exponents of Rational Homotopy Groups (2007) (2)
- Sequential weak approximation for maps of finite Hessian energy (2013) (1)
- Elliptic Operators in Weighted Hölder Spaces (2000) (1)
- Three-commutators revisited (2020) (1)
- Morse Index Stability for Critical Points to Conformally invariant Lagrangians (2022) (1)
- A variational approach to $S^1$-harmonic maps and applications (2021) (1)
- Pointwise Expansion of Degenerating Immersions of Finite Total Curvature (2022) (1)
- The Unique Tangent Cone Property for Weakly Holomorphic Maps into Projective Algebraic Varieties (2021) (1)
- Harmonic Maps from S into S with low Morse Index (2019) (0)
- Weak Holomorphic Structures over Kähler Surfaces (2019) (0)
- D G ] 1 1 M ay 2 01 4 Tori in S 3 minimizing locally the conformal volume (2014) (0)
- A pr 2 00 6 PARTIAL REGULARITY FOR HARMONIC MAPS , AND RELATED PROBLEMS (2020) (0)
- Towards Jaffe and Taubes Conjectures (2000) (0)
- Elliptic Operators in Weighted Sobolev Spaces (2000) (0)
- Sequential weak approximation for maps of finite Hessian energy (2015) (0)
- Existence of Ginzburg-Landau Vortices (2000) (0)
- Solving Uniqueness Questions (2000) (0)
- Generalized Pohozaev Formula for ρ-Conformal Fields (2000) (0)
- ec 2 00 6 Analysis aspects of Willmore surfaces (2008) (0)
- 2 8 A pr 2 00 6 PARTIAL REGULARITY FOR HARMONIC MAPS , AND RELATED PROBLEMS (2006) (0)
- Embedded Surfaces of Arbitrary Genus Minimizing the Willmore Energy Under Isoperimetric Constraint (2013) (0)
- Mapping Properties of L ε (2000) (0)
- Qualitative Aspects of Ginzburg-Landau Equations (2000) (0)
- A viscosity method in the min-max theory of minimal surfaces (2017) (0)
- Effects de quantification pour -Δu=u(1-|u|2) sur R2 (1993) (0)
- The Linearized Operator about the Approximate Solution ũ (2000) (0)
- Uniform regularity results for critical and subcritical surface energies (2018) (0)
- Sujet: Optimal transport, Euler equations, (2009) (0)
- Critical Chirality in Elliptic Systems (2019) (0)
- Families of Approximate Solutions with Prescribed Zero Set (2000) (0)
- The Role of Zeros in the Uniqueness Question (2000) (0)
- Existence of infinitely many minimal hypersurfaces in low dimensions, after F.C. Marques, A.A. Neves et A. Song (Bourbaki Seminar) (2019) (0)
- Almost Monotonicity Formula for H-minimal Legendrian Surfaces in the Heisenberg Group (2021) (0)
- A Resolution of the Poisson Problem for Elastic Plates (2020) (0)
- Inequalities and A Priori Estimates (2015) (0)
- Integrability by compensation for Dirac equation (2021) (0)
- Sobolev connections and holomorphic structures over Kähler surfaces (2021) (0)
- 3-Commutators Revisited (2019) (0)
- The fractional Liouville equation in dimension 1 Geometry, Compactness and quantization (Analysis on Shapes of Solutions to Partial Differential Equations) (2018) (0)
- The regularity of conformal target harmonic maps (2017) (0)
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