Published Paper

Inserted: 23 jan 2019
Last Updated: 29 sep 2024

Journal: Advances in Mathematics
Year: 2020

This is a further work after http:/cvgmt.sns.itpaper3594

All comments are welcome !

Abstract:

In this paper we investigate Lott-Sturm-Villani's synthetic lower Ricci curvature bound on Riemannian manifolds with boundary. We prove several new measure rigidity results, which completely characterize ${\rm CD}(K, \infty)$ condition and non-collapsed ${\rm CD}(K, N)$ condition on Riemannian manifolds with boundary. In particular, using recent results on $L^1$-optimal transportation theory, we prove that ${\rm CD}(K, \infty)$ condition implies geodesical convexity of the support of the reference measure.

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• 10. @AIM20@Measure rigidity of synthetic lower Ricci curvature bound on Riemannian manifolds.pdf