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The Monge–Ampère Equation and Its Applications

https://doi.org/10.4171/170
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On the prescribed negative Gauss curvature problem for graphs
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A personal tribute to Louis Nirenberg: February 28, 1925–January 26, 2020.
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Convex radial solutions for Monge-Amp$ \grave{\text e} $re equations involving the gradient
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Games associated with products of eigenvalues of the Hessian
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Global regularity for the Monge-Ampère equation with natural boundary condition
inferred← citeshttps://doi.org/10.4153/s0008414x24000725openalex-snapshot
Alexandrov’s estimate revisited
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Additive kinematic formulas for convex functions
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JKO estimates in linear and non-linear Fokker–Planck equations, and Keller–Segel: $L^p$ and Sobolev bounds
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A spectral characterization and an approximation scheme for the Hessian eigenvalue
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Обзор по точным решениям и редукциям уравнений типа Монжа-Ампера
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On Symmetry Reduction of the (1 + 3)-Dimensional Inhomogeneous Monge-Ampère Equation to the First-Order ODEs
inferred← citeshttps://doi.org/10.48550/arxiv.1803.02799openalex-snapshot
Projective Hessian and Sasakian manifolds
inferred← citeshttps://doi.org/10.48550/arxiv.1809.05421openalex-snapshot
Existence of entire solutions of Monge-Ampère equations with prescribed asymptotic behaviors
inferred← citeshttps://doi.org/10.48550/arxiv.1811.12531openalex-snapshot
Global $W^{2,1+\varepsilon}$ estimates for Monge-Ampère equation with natural boundary condition
inferred← citeshttps://doi.org/10.48550/arxiv.1905.10812openalex-snapshot
Regularity as Regularization: Smooth and Strongly Convex Brenier Potentials in Optimal Transport
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Regularity of fully non-linear elliptic equations on Hermitian manifolds. II
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Entropic Optimal Transport between Unbalanced Gaussian Measures has a Closed Form
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q-Moment Measures and Applications: A New Approach via Optimal Transport
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Synthetic MTW conditions and their equivalence under mild regularity assumption on the cost function
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A Consistent Extension of Discrete Optimal Transport Maps for Machine Learning Applications
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Translating surfaces under flows by sub-affine-critical powers of Gauss curvature
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Remembering Louis Nirenberg and his mathematics
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New links between PDE's and Voronoi patterns
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Singular Monge-Ampere equations over convex domains
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A Nonlinear Mean Value Property for the Monge-Ampère Operator
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Statistical analysis of the optimal transport problem
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Contributions to the optimal transport problem and its regularity
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Unveiling the Transport Dynamics of Neural Networks : a Least Action Principle for Deep Learning
inferred← citeshttps://doi.org/10.70675/7b0b5fcfzc6cfz4804zbe51z9043f09b5382openalex-snapshot
Neural Models for Learning Real World Dynamics and the Neural Dynamics of Learning
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Machine learning over spaces of measures : invariant deep networks and quantile regression
inferred← citeshttps://doi.org/10.70675/be1029f0zd58az415fz8847zc2557adefa96openalex-snapshot
Sur les gaz de Coulomb et le transport optimal multimarge
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Optimal transport in high dimension : obtaining regularity and robustness using convexity and projections
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Leveraging regularization, projections and elliptical distributions in optimal transport
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