Asian Journal of Mathematics

Volume 17 (2013)

Number 3

Remarks on a scalar curvature rigidity theorem of Brendle and Marques

Pages: 457 – 470

DOI: http://dx.doi.org/10.4310/AJM.2013.v17.n3.a4

Authors

Graham Cox (Department of Mathematics, Duke University, Durham, NC 27708, U.S.A.)

Pengzi Miao (School of Mathematical Sciences, Monash University, Victoria, Australia; Department of Mathematics, University of Miami, Coral Gables, Florida, U.S.A.)

Luen-Fai Tam (Institute of Mathematical Sciences and Department of Mathematics, Chinese University of Hong Kong, Shatin, Hong Kong)

Abstract

We give an improvement of a scalar curvature rigidity theorem of Brendle and Marques regarding geodesic balls in $\mathbb{S}^n$. The main result is that Brendle and Marques’ theorem holds on a geodesic ball larger than that specified in [2].

Keywords

scalar curvature, mean curvature, Min-Oo’s conjecture

2010 Mathematics Subject Classification

53C20, 53C24

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