Anal.Math.Phys. https://doi.org/10.1007/s13324-018-0237-5 Boundary effect of m-dimensional Bakry-Émery Ricci curvature 1 2 Qiang Tu · Guangyue Huang Received: 23 June 2017 / Revised: 24 March 2018 / Accepted: 27 May 2018 © Springer International Publishing AG, part of Springer Nature 2018 Abstract We consider how m-dimensional Bakry-Émery Ricci curvature affects the geometry of the boundary ∂ M. By using the Reilly’s formula with respect to f -Laplacian, geometric inequalities involving f -mean curvature are obtained. Fur- thermore, we also achieve the relationship between f -mean curvature of the boundary submanifold and the mean curvature of submanifold x : ∂ M → R (c) into space form R (c). Keywords f -mean curvature · Boundary effect · m-dimensional Bakry-Émery Ricci curvature Mathematics Subject Classiﬁcation Primary 53C42; Secondary 53C21 1 Introduction Let (M, g) be an n-dimensional compact Riemannian manifold with nonempty smooth boundary ∂ M.In, Miao and Wang consider the question how the Ricci curva- The research of authors is supported by Hubei Key Laboratory of Applied Mathematics (Hubei University) and NSFC(No. 11371018, 11671121). B Qiang Tu firstname.lastname@example.org Guangyue Huang email@example.com Faculty of Mathematics and Statistics, Hubei University, Wuhan 430062, People’s Republic of China Department of Mathematics, Henan Normal University, Xinxiang
Analysis and Mathematical Physics – Springer Journals
Published: May 30, 2018
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