6533b824fe1ef96bd12800a4

RESEARCH PRODUCT

Optimal maps and exponentiation on finite dimensional spaces with Ricci curvature bounded from below

Tapio RajalaKarl-theodor SturmNicola GigliNicola Gigli

subject

Mathematics - Differential GeometryExponentiationLower Ricci bounds; Optimal maps; Optimal transport; RCD spaces01 natural sciencesMeasure (mathematics)Combinatoricssymbols.namesakeMathematics - Metric GeometryRCD spacesSettore MAT/05 - Analisi MatematicaFOS: MathematicsOptimal transportMathematics::Metric GeometryUniqueness0101 mathematicsLower Ricci bounds[MATH.MATH-MG]Mathematics [math]/Metric Geometry [math.MG]Ricci curvatureMathematicsDiscrete mathematics010102 general mathematicsMetric Geometry (math.MG)Absolute continuity16. Peace & justice010101 applied mathematicsMathematics::LogicDifferential geometryDifferential Geometry (math.DG)Fourier analysisBounded functionsymbolsOptimal mapsGeometry and Topology

description

We prove existence and uniqueness of optimal maps on $RCD^*(K,N)$ spaces under the assumption that the starting measure is absolutely continuous. We also discuss how this result naturally leads to the notion of exponentiation.

yearjournalcountryeditionlanguage
2013-05-21
10.1007/s12220-015-9654-yhttp://hdl.handle.net/20.500.11767/15788