SU\G(𝔾)/K·U
Mathematics â€ș Applied Mathematics

Optimal Transport in Geometry and Analysis

Works Count: 66967

Description

This cluster of papers explores the mathematical theory and applications of optimal transport, including topics such as Ricci curvature, Wasserstein distance, metric measure spaces, gradient flows, Sobolev inequalities, the Monge-Kantorovich problem, mean curvature flow, and minimal surfaces.

Keywords

Optimal Transport; Ricci Curvature; Wasserstein Distance; Metric Measure Spaces; Gradient Flows; Sobolev Inequalities; Monge-Kantorovich Problem; Mean Curvature Flow; Geometric Applications; Minimal Surfaces

Most Cited Works

Action Title Date Authors
+
Metric Structures for Riemannian and Non-Riemannian Spaces 2007-01-01 Mikhael Gromov
+ PDF Ask
Flow by mean curvature of convex surfaces into spheres 1984-01-01 Gerhard Huisken
+ PDF Ask
The heat equation shrinks embedded plane curves to round points 1987-01-01 M. Grayson
+
Riemannian Geometry and Geometric Analysis 1998-01-01 JĂŒrgen Jost
+ PDF Ask
Contact Manifolds in Riemannian Geometry 1976-01-01 David E. Blair
+ PDF Ask
Three-manifolds with positive Ricci curvature 1982-01-01 Richard S. Hamilton
+ PDF Ask
The heat equation shrinking convex plane curves 1986-01-01 Michael E. Gage Richard S. Hamilton
+
Numerical Approximation of Hyperbolic Systems of Conservation Laws 1996-01-01 Edwige Godlewski Pierre-Arnaud Raviart
+ PDF Ask
Introduction to Smooth Manifolds 2012-01-01 John M. Lee
+
Fully Nonlinear Elliptic Equations 1995-09-22 Luis Caffarelli Xavier Cabré
+ PDF Ask
Lectures on Quasiconformal Mappings 2006-07-14 Lars V. Ahlfors
+
The Self-Duality Equations on a Riemann Surface 1987-07-01 Nigel Hitchin
+ PDF Ask
Riemannian Geometry of Contact and Symplectic Manifolds 2010-01-01 David E. Blair
+
Existence and Uniqueness of the Minimizing Solution of Choquard's Nonlinear Equation 1977-10-01 Élliott H. Lieb
+
A Course in Metric Geometry 2001-06-12 Dmitri Burago Yuri Burago S. V. Ivanov
+
Harmonic functions on complete riemannian manifolds 1975-03-01 Shing‐Tung Yau
+ PDF Ask
Ricci curvature for metric-measure spaces via optimal transport 2009-04-22 John Lott CĂ©dric Villani
+ PDF Ask
On the parabolic kernel of the Schrödinger operator 1986-01-01 Peter Li Shing Tung Yau
+ PDF Ask
The entropy formula for the Ricci flow and its geometric applications 2002-01-01 Grisha Perelman
+
Harmonic Mappings of Riemannian Manifolds 1964-01-01 James Eells J. H. Sampson
+ PDF Ask
Computing Discrete Minimal Surfaces and Their Conjugates 1993-01-01 Ulrich Pinkall Konrad Polthier
+ PDF Ask
Real hypersurfaces in complex manifolds 1974-01-01 Shiing-Shen Chern JĂŒrgen Moser
+
On the variational principle 1974-08-01 Ivar Ekeland
+ PDF Ask
The Yamabe problem 1987-01-01 John M. Lee Thomas H. Parker
+
A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem 2000-01-01 Jean‐David Benamou Yann Brenier
+ PDF Ask
Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations 1988-11-01 Stanley Osher James A. Sethian
+ PDF Ask
Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des fluides parfaits 1966-01-01 Vladimir I. Arnold
+ PDF Ask
Generalized gradients and applications 1975-01-01 Frank H. Clarke
+
Curvatures of left invariant metrics on lie groups 1976-09-01 John Milnor
+ PDF Ask
On the geometry of metric measure spaces. II 2006-01-01 Karl‐Theodor Sturm
+
Some Nonlinear Problems in Riemannian Geometry 1998-01-01 Thierry Aubin
+
Pseudo holomorphic curves in symplectic manifolds 1985-06-01 M. Gromov
+ PDF Ask
On the proof of the positive mass conjecture in general relativity 1979-02-01 Richard Schoen Shing-Tung Yau
+ PDF Ask
Three dimensional manifolds, Kleinian groups and hyperbolic geometry 1982-05-01 William P. Thurston
+
THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION 2001-01-31 FĂ©lix Otto
+ PDF Ask
Persistence and Smoothness of Invariant Manifolds for Flows 1971-01-01 Neil Fenichel
+ PDF Ask
Manifolds of negative curvature 1969-01-01 Richard L. Bishop Barrett O’Neill
+
The Variational Formulation of the Fokker--Planck Equation 1998-01-01 Richard W. Jordan David Kinderlehrer FĂ©lix Otto
+ PDF Ask
Motion of level sets by mean curvature. I 1991-01-01 L. C. Evans Joel Spruck
+
On the ricci curvature of a compact kĂ€hler manifold and the complex monge‐ampĂ©re equation, I 1978-05-01 Shing–Tung Yau
+
Minimal Varieties in Riemannian Manifolds 1968-07-01 James Simons
+
Spectral asymmetry and Riemannian Geometry. I 1975-01-01 Michael Atiyah V. K. Patodi I. M. Singer
+
Polar factorization and monotone rearrangement of vector‐valued functions 1991-06-01 Yann Brenier
+ PDF Ask
Conformal deformation of a Riemannian metric to constant scalar curvature 1984-01-01 Richard Schoen
+ PDF Ask
Ricci flow with surgery on three-manifolds 2003-01-01 Grisha Perelman
+
Global Lorentzian Geometry 2017-09-29 John K. Beem Paul E. Ehrlich Kevin L. Easley
+ PDF Ask
Singular hypersurfaces and thin shells in general relativity 1967-04-01 W. Israel
+
Optimal Transport 2008-10-25 CĂ©dric Villani
+ PDF Ask
Invariant Manifolds 1977-01-01 Morris W. Hirsch Charles Pugh Michael Shub
+
Einstein Manifolds 1987-01-01 Arthur L. Besse

Most Recent Works

Action Title Date Authors
+
Characterization of Almost Complex Manifolds and KĂ€hler Geometry 2025-04-30 Md Shapan Miah Khondokar M Ahmed
+
Riemann solitons on imperfect fluid spacetimes 2025-04-30 Shahroud Azami Uday Chand De
+
On hypersurfaces of $\mathbb{S}^2\times \mathbb{S}^2$ and $\mathbb{H}^2\times \mathbb{H}^2$ with recurrent Ricci tensor 2025-04-30 Qianshun Cui Zejun Hu Xiaojuan Lu Zeke Yao
+
The Ideal Circle Pattern with Boundaries via Analytic Method 2025-05-02 Haoyong Yu
+
Logarithmic vanishing theorems on weakly 1-complete KĂ€hler manifolds 2025-05-02 Shilong Lu
+
Dynamics of convex mean curvature flow 2025-05-02 Sigurd B Angenent Panagiota Daskalopoulos NataĆĄa Ć eĆĄum
+
Colding–Minicozzi entropies in Cartan–Hadamard manifolds 2025-05-02 Jacob Bernstein Arunima Bhattacharya
+
Heat kernel estimates and their stabilities for symmetric jump processes with general mixed polynomial growths on metric measure spaces 2025-05-02 Joohak Bae Jae-Hoon Kang Panki Kim Jaehun Lee
+
Restriction Estimates for Hyperbolic Paraboloids in Higher Dimensions 2025-05-02 Zhuoran Li
+ PDF Ask
Schwarz symmetrizations in parabolic equations on complete manifolds 2025-04-30 Haiqing Cheng Tengfei Ma Kui Wang
+ PDF Ask
Volume gap between the minimal submanifold and the unit sphere 2025-04-30 Wei Ding Jianquan Ge Fagui Li
+
The vacuum weighted Einstein field equations 2025-05-03 Miguel Brozos‐Vázquez Diego Mojón-Álvarez
+
Finite elements for Wasserstein $\mathbb{W}_p$ gradient flows 2025-05-03 Clément CancÚs Daniel Matthes Flore Nabet Eva-Maria Rott
+
A variational approach to the Hermitian–Einstein metrics and the Quot-scheme limit of Fubini–Study metrics 2025-05-03 Yoshinori Hashimoto Julien Keller
+
Smooth local solutions to the degenerate hyperbolic Gauss–Codazzi system 2025-05-04 Yanbo Hu Houbin Guo Xiaolong Qin
+ PDF Ask
Weak solutions to gradient flows of functionals with inhomogeneous growth in metric spaces 2025-05-04 Wojciech GĂłrny
+
Analytical and Geometric Foundations and Modern Applications of Kinetic Equations and Optimal Transport 2025-05-04 CĂ©cile Barbachoux Joseph Kouneiher
+ PDF Ask
Optimal metrics for the first curl eigenvalue on 3-manifolds 2025-05-05 Alberto Enciso Wadim Gerner Daniel Peralta‐Salas
+
Constant Scalar Curvature KĂ€hler Metrics on Resolutions of an Orbifold Singularity of Depth 1 2025-05-05 Mehrdad Najafpour
+
Dirichlet Scalar Determinants on Two-Dimensional Constant Curvature Disks 2025-05-05 Soumyadeep Chaudhuri Frank D. Ferrari
+
On discrete affine invariants of PL curves in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msup></mml:math> 2025-05-01 Ya. V. BazaÄ­kin Alexei Kotov
+ PDF Ask
Curve shortening flow with an ambient force field 2025-05-05 Samuel Cuthbertson Glen Wheeler Valentina‐Mira Wheeler
+
Generalized Pseudo-Ricci–Yamabe solitons on real hypersurfaces in the complex hyperbolic two-plane Grassmannians 2025-05-03 Young Jin Suh
+
Metric extrapolation in the Wasserstein space 2025-05-05 Thomas Gallouët Andrea Natale Gabriele Todeschi
+
Comparison theorems on H-type sub-Riemannian manifolds 2025-05-05 Fabrice Baudoin Erlend Grong Luca Rizzi Gianmarco Vega-Molino
+
Large deviations for the volume of hyperbolic k-nearest neighbor balls 2025-05-01 Christian Hirsch Moritz Otto Takashi Owada Christoph ThÀle
+
Nonnegative Ricci curvature, almost stability at infinity, and structure of fundamental groups 2025-05-06 Jiayin Pan
+
The half-volume spectrum of a manifold 2025-05-07 Liam Mazurowski Xin Zhou
+
Weighted Extremal Metrics on Blowups 2025-05-06 Michael Hallam
+
Poincaré Type Results on a k-Dimensional Torus 2025-05-01 Lev Sakhnovich
+
A precise determination of the contact CR $$\delta $$-invariant for typical submanifolds within a Lorentz-Sasakian space form 2025-05-06 Octavian Postavaru Ion Mihai
+
Infinite-length limit of spectral curves and inverse scattering 2025-05-05 Niklas Beisert Kunal Gupta
+
Non-compact Einstein manifolds with unimodular isometry group 2025-05-06 Christoph Böhm R Lafuente
+
Remarks on the spectra of minimal hypersurfaces in the hyperbolic space 2025-05-06 Gerasim Kokarev
+
An investigation into W9 - curvature tensor in Lorentzian ÎČ - Kenmotsu manifolds 2025-05-01 Rohit Chaudhary P. K. Singh
+
Intermediate spaces on weak type discrete Morrey spaces 2025-05-05 Rizma Yudatama ‎Denny Ivanal Hakim
+
Stochastically complete constant mean curvature spacelike hypersurfaces in Generalized Robertson-Walker spacetimes 2025-05-01 Mårio Medina José A. S. Pelegrín
+
Multiplicity results for mass constrained Allen–Cahn equations on Riemannian manifolds with boundary 2025-05-07 Dario Corona Stefano Nardulli Ramon Oliver-Bonafoux Giandomenico Orlandi P. Piccione
+
Lusin approximation for functions of bounded variation 2025-05-08 Panu Lahti Khanh Ngoc Nguyen
+
A Toponogov globalisation result for Lorentzian length spaces 2025-05-07 Tobias Beran John Harvey Lewis Napper Felix Rott
+
SOME RESULTS ON GENERALIZED $$\eta $$-RICCI SOLITONS 2025-05-07 Amalendu Ghosh
+ PDF Ask
Monge–Ampùre geometry and the Eady problem 2025-05-01 Roberto D’Onofrio G. Ortenzi Ian Roulstone
+
On the boundary criterion for relative cubulation: Multiended parabolics 2025-05-08 Eduard Einstein Suraj Krishna M S Thomas Ng
+
On the Convergence Rate of Sinkhorn’s Algorithm 2025-05-08 Promit Ghosal Marcel Nutz
+
Integrable Corners in the Space of Gukov-Witten Surface Defects 2025-05-01 Adam Chalabi Charlotte Kristjansen Chenliang Su
+
CL-Transformation on 3-Dimensional Quasi Sasakian Manifolds and Their Ricci Soliton 2025-05-08 Rajesh Kumar Lalnunenga Colney Dalal Alhwikem
+
Anomalous dimensions in the symmetric orbifold 2025-05-09 Matthias R. Gaberdiel Felix Lichtner Beat Nairz
+ PDF Ask
Subordinated Bessel heat kernels 2025-05-09 Krzysztof Bogdan Konstantin Merz
+
Quantitative stability for complex Monge–Ampùre equations, I 2025-05-10 Hoang-Son Do Duc‐Viet Vu
+
The Gauss Minkowski problem for unbounded closed convex sets 2025-05-10 Bin Chen Wei Shi