Manifolds with non-negative bakry-émery ricci curvature and minimal boundary

Ning Yang; Jia Ping Wang

doi:10.1090/proc/14418

Manifolds with non-negative bakry-émery ricci curvature and minimal boundary

Ning Yang, Jia Ping Wang

School of Mathematics

Research output: Contribution to journal › Article › peer-review

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Abstract

In this note, we prove that a non-compact Riemannian manifold M with non-negative Bakry-Émery Ricci curvature and compact minimal boundary ?M is the isometric product ∂M ×[0,∞), provided that the potential function is bounded from above and has non-negative derivatives at ∂M along inner normal directions.

Original language	English (US)
Pages (from-to)	2207-2212
Number of pages	6
Journal	Proceedings of the American Mathematical Society
Volume	147
Issue number	5
DOIs	https://doi.org/10.1090/proc/14418
State	Published - May 2019

Bibliographical note

Funding Information:
Received by the editors August 17, 2018, and, in revised form, October 2, 2018. 2010 Mathematics Subject Classification. Primary 53C20, 53C21. The author was partially supported by the Natural Science Research grant 17KJD110007 for Institutions of Higher Education of Jiangsu Province, China.

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© 2019 American Mathematical Society.

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N2 - In this note, we prove that a non-compact Riemannian manifold M with non-negative Bakry-Émery Ricci curvature and compact minimal boundary ?M is the isometric product ∂M ×[0,∞), provided that the potential function is bounded from above and has non-negative derivatives at ∂M along inner normal directions.

AB - In this note, we prove that a non-compact Riemannian manifold M with non-negative Bakry-Émery Ricci curvature and compact minimal boundary ?M is the isometric product ∂M ×[0,∞), provided that the potential function is bounded from above and has non-negative derivatives at ∂M along inner normal directions.

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Manifolds with non-negative bakry-émery ricci curvature and minimal boundary

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