Artículo
Polar factorization of conformal and projective maps of the sphere in the sense of optimal mass transport
Fecha de publicación:
04/2018
Editorial:
Hebrew Univ Magnes Press
Revista:
Israel Journal Of Mathematics
ISSN:
0021-2172
e-ISSN:
1565-8511
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
Let M be a compact Riemannian manifold and let μ,d be the associated measure and distance on M. Robert McCann, generalizing results for the Euclidean case by Yann Brenier, obtained the polar factorization of Borel maps S : M -> M pushing forward μ to a measure ν: each S factors uniquely a.e. into the composition S = T circ U, where U : M -> M is volume preserving and T : M -> M is the optimal map transporting μ to ν with respect to the cost function d^2/2. In this article we study the polar factorization of conformal and projective maps of the sphere S^n. For conformal maps, which may be identified with elements of the identity component of O(1,n+1), we prove that the polar factorization in the sense of optimal mass transport coincides with the algebraic polar factorization (Cartan decomposition) of this Lie group. For the projective case, where the group GL_+(n+1) is involved, we find necessary and sufficient conditions for these two factorizations to agree.
Archivos asociados
Licencia
Identificadores
Colecciones
Articulos(CIEM)
Articulos de CENT.INV.Y ESTUDIOS DE MATEMATICA DE CORDOBA(P)
Articulos de CENT.INV.Y ESTUDIOS DE MATEMATICA DE CORDOBA(P)
Citación
Godoy, Yamile Alejandra; Salvai, Marcos Luis; Polar factorization of conformal and projective maps of the sphere in the sense of optimal mass transport; Hebrew Univ Magnes Press; Israel Journal Of Mathematics; 225; 1; 4-2018; 465-478
Compartir
Altmétricas