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This article addresses regularity of optimal transport maps for cost=“squared distance” on Riemannian manifolds that are products of arbitrarily many round spheres with arbitrary sizes and dimensions. Such manifolds are known to be non-negatively cross-curved. Under boundedness and non-vanishing assumptions on the transfered source and target densities we show that optimal maps stay away from the cut-locus (where the cost exhibits singularity), and obtain injectivity and continuity of optimal maps....

Regularity of p-harmonic maps into certain manifolds with positive sectional curvature.

Y.L. Xin, Yang Yihu (1995)

Journal für die reine und angewandte Mathematik

Regularly metrizable connections and tensors of type (1,3) (Preliminary communication)

Oldřich Kowalski (1971)

Commentationes Mathematicae Universitatis Carolinae

Relèvements Dans Le Fibré Conormal D'Un Feuilletage D'Une Variété Riemannienne

Tong Van Duc (1991)

Publications de l'Institut Mathématique

Remark on the Helly Number for Strongly Convex Sets on Riemannian Manifolds.

Norbert Kleinjohann (1981)

Manuscripta mathematica

Remarks on holomorphic vector fields on non-compact manifolds

Giuliana Gigante (1974)

Rendiconti del Seminario Matematico della Università di Padova

Remarks on the Yamabe problem and the Palais-Smale condition

D. Fortunato, G. Palmieri (1986)

Rendiconti del Seminario Matematico della Università di Padova

Remarques sur les variétés conformément plates.

Jacques Lafontaine (1982)

Mathematische Annalen

Report on M. Gromov's almost flat manifolds

Hermann Karcher (1978/1979)

Séminaire Bourbaki

Représentations de $G^{X}$ (G compact) selon Verchik-Gelfand-Graiev et Ismagilov

Alain Guichardet (1978/1979)

Séminaire Bourbaki

Representations of Compact Lie Groups and Elliptic Operators.

Ernst Heintze, Jochen Brüning (1978/1979)

Inventiones mathematicae

Representations of the group of functions taking values in a compact Lie group

I. M. Gelfand, M. I. Graev, A. M. Veršik (1980)

Compositio Mathematica

Resolvent Flows for Convex Functionals and p-Harmonic Maps

Kazuhiro Kuwae (2015)

Analysis and Geometry in Metric Spaces

We prove the unique existence of the (non-linear) resolvent associated to a coercive proper lower semicontinuous function satisfying a weak notion of p-uniform λ-convexity on a complete metric space, and establish the existence of the minimizer of such functions as the large time limit of the resolvents, which generalizing pioneering work by Jost for convex functionals on complete CAT(0)-spaces. The results can be applied to Lp-Wasserstein space over complete p-uniformly convex spaces. As an application,...

Ricci curvature and qusiconformal deformations of a Riemannian manifold.

Antoni Pierzchalski (1990)

Manuscripta mathematica

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