Second order variational heuristics for the Monge problem on compact manifolds

DOI10.1515/acv.2011.017zbMath1248.49058OpenAlexW2328267777MaRDI QIDQ2903477

Philippe P. Delanoë

Publication date: 10 August 2012

Published in: Advances in Calculus of Variations (Search for Journal in Brave)

Full work available at URL: https://hal.univ-cotedazur.fr/hal-00613698v2/file/Delanoe_2ndVarHeurist-Monge.pdf

zbMATH Keywords

Monge problem\(c\)-convexitysecond order variation\(c\)-Hessian positivity\(c\)-potentialminimizing diffeomorphism

Mathematics Subject Classification ID

Differential geometric aspects in vector and tensor analysis (53A45) Variational problems in a geometric measure-theoretic setting (49Q20) Groups of diffeomorphisms and homeomorphisms as manifolds (58D05) Existence theories for problems in abstract spaces (49J27) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Variational problems in infinite-dimensional spaces (58E99)

Cites Work

• The geometry of optimal transportation
• Regularity of potential functions of the optimal transportation problem
• Groups of diffeomorphisms and the motion of an incompressible fluid
• Variational Heuristics for Optimal Transportation Maps on Compact Manifolds
• Polar factorization of maps on Riemannian manifolds