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Comparison Geometry of Manifolds with Boundary under a Lower Weighted Ricci Curvature Bound

Part of: Global differential geometry

Published online by Cambridge University Press:  24 October 2018

Yohei Sakurai
Yohei Sakurai*
Affiliation:
Advanced Institute for Materials Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai, 980-8577, Japan Email: [email protected]
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Abstract

We study Riemannian manifolds with boundary under a lower weighted Ricci curvature bound. We consider a curvature condition in which the weighted Ricci curvature is bounded from below by the density function. Under the curvature condition and a suitable condition for the weighted mean curvature for the boundary, we obtain various comparison geometric results.

Keywords

Manifold with boundaryWeighted Ricci curvature

MSC classification

Primary: 53C20: Global Riemannian geometry, including pinching
Type
Article
Information
Canadian Journal of Mathematics , Volume 72 , Issue 1 , February 2020 , pp. 243 - 280
Copyright
© Canadian Mathematical Society 2018 

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Footnotes

Research Fellow of Japan Society for the Promotion of Science for 2014–2016

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