Communications in Analysis and Geometry

Volume 17 (2009)

Number 1

Large-sphere and small-sphere limits of the Brown-York mass

Pages: 37 – 72



Xu-Qian Fan (Department of Mathematics, Jinan University, China)

Yuguang Shi (Key Laboratory of Pure and Applied Mathematics, School of Mathematics Science, Peking University)

Luen-Fai Tam (Institute of Mathematical Sciences, The Chinese University of Hong Kong)


In this paper, we will study the limiting behavior of theBrown--York mass of the coordinate spheres in an asymptoticallyflat manifold. Limiting behaviors of volumes of regions relatedto coordinate spheres are also obtained, including a discussion onthe isoperimetric mass introduced by Huisken \cite{Huisken}. Wewill also study expansions of the Brown--York mass and the Hawking mass of geodesic spheres with center at afixed point $p$ of a 3-manifold. Some geometric consequenceswill be derived.

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