Polar factorization of maps on Riemannian manifolds | Zendy

Robert J. McCann | Zendy

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Polar factorization of maps on Riemannian manifolds

Author(s) -

Robert J. McCann

Publication year - 2001

Publication title -

geometric and functional analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 3.952

H-Index - 77

eISSN - 1420-8970

pISSN - 1016-443X

DOI - 10.1007/pl00001679

Subject(s) - mathematics , riemannian manifold , nabla symbol , combinatorics , factorization , polar decomposition , space (punctuation) , boundary (topology) , euclidean space , polar , mathematical analysis , physics , omega , algorithm , astronomy , linguistics , philosophy , quantum mechanics

Let (M; g) be a connected compact manifold, C3smooth and withoutboundary, equipped with a Riemannian distance d(x; y). If s : M \Gamma! M ismerely Borel and never maps positive volume into zero volume, we show s = tffiufactors uniquely a.e. into the composition of a map t(x) = exp x [\Gammar/(x)] anda volume-preserving map u : M \Gamma! M , where / : M \Gamma! R is an infimalconvolution with c(x; y) = d2(x; y)=2. Like the factorization it generalizes fromEuclidean space,...

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