Gradient rearrangement for diffeomorphisms of a compact manifold.

DOI10.1016/j.difgeo.2003.10.003zbMath1039.58008OpenAlexW2054601767WikidataQ115358112 ScholiaQ115358112MaRDI QIDQ1426668

Philippe P. Delanoë

Publication date: 15 March 2004

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.difgeo.2003.10.003

zbMATH Keywords

diffeomorphismcomparison principlerearrangementfactorizationgradient mappingmeasure preservingHelm\-holtz decomposition

Mathematics Subject Classification ID

Maximum principles in context of PDEs (35B50) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Variational inequalities (global problems) in infinite-dimensional spaces (58E35) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items

Regularity of optimal transport on compact, locally nearly spherical, manifolds, Regularity of optimal transport maps on multiple products of spheres, On the regularity of solutions of optimal transportation problems, A Perturbative Approach to the Parabolic Optimal Transport Problem, Lie solutions of Riemannian transport equations on compact manifolds, A perturbation argument for a Monge-Ampère type equation arising in optimal transportation, Gradient estimates for potentials of invertible gradient-mappings on the sphere, Continuity, curvature, and the general covariance of optimal transportation, Regularity of optimal maps on the sphere: the quadratic cost and the reflector antenna, Stability of a 4th-order curvature condition arising in optimal transport theory, Continuity of optimal transport maps and convexity of injectivity domains on small deformations of 𝕊², Differential Geometric Heuristics for Riemannian Optimal Mass Transportation, Erratum to: ``Gradient rearrangement for diffeomorphisms of a compact manifold, Towards the smoothness of optimal maps on Riemannian submersions and Riemannian products (of round spheres in particular)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Equations du type Monge-Ampère sur les variétés Riemanniennes compactes. I
• Equations du type de Monge-Ampère sur les variétés Riemanniennes compactes. II
• Equations du type de Monge-Ampère sur les variétés Riemanniennes compactes. III
• Classical solvability in dimension two of the second boundary-value problem associated with the Monge-Ampère operator
• A Riemannian interpolation inequality à la Borell, Brascamp and Lieb
• Formes-volume sur les variétés à bord
• Perturbing fully nonlinear second order elliptic equations.
• The index of elliptic operators. I
• Groups of diffeomorphisms and the motion of an incompressible fluid
• Polar factorization and monotone rearrangement of vector‐valued functions
• The Regularity of Mappings with a Convex Potential
• Some regularity properties of solutions of Monge Ampère equation
• Sur le transport de mesures périodiques
• On the second boundary value problem for equations of Monge-Ampère type.
• Nondivergent elliptic equations on manifolds with nonnegative curvature
• On the Volume Elements on a Manifold
• Polar factorization of maps on Riemannian manifolds