Topic
Scalar curvature
About: Scalar curvature is a research topic. Over the lifetime, 12701 publications have been published within this topic receiving 296040 citations. The topic is also known as: Ricci scalar.
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Journal Article•
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88 citations
TL;DR: In this article, the authors define a notion of mean curvature for hypersurfaces and show that the boundary of a stationary set is a constant mean curvatures (CMC) hypersurface.
Abstract: In this article we study sets in the (2n + 1)-dimensional Heisenberg group ℍnwhich are critical points, under a volume constraint, of the sub-Riemannian perimeter associated to the distribution of horizontal vector fields in ℍn.We define a notion of mean curvature for hypersurfaces and we show that the boundary of a stationary set is a constant mean curvature (CMC) hypersurface. Our definition coincides with previous ones.
88 citations
TL;DR: In this article, local gradient and Laplacian estimates of the Aronson-Benilan and Li-Yau type for positive solutions of porous medium equations posed on Riemannian manifolds with a lower Ricci curvature bound were derived.
88 citations