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

• DOI: 10.4310/cag.2009.v17.n1.a3
• Publication Date: 2013-08-30T22:25:02Z
• Authors: Xu-Qian Fan; Yuguang Shi; Luen-Fai Tam
• Keywords: Mathematics - Differential Geometry; Differential Geometry (math.DG); FOS: Mathematics; FOS: Physical sciences; Secondary 83C99; Mathematical Physics (math-ph); 0101 mathematics; Primary 53C20; Secondary 83C99; 01 natural sciences; Mathematical Physics; Primary 53C20

32pages, no figure<br/>In this paper, we will study the limiting behavior of the Brown-York mass of the coordinate spheres in an asymptotically flat manifold. Limiting behaviors of volumes of regions related to coordinate spheres are also obtained, including a discussion on the isoperimetric mass introduced by Huisken \cite{Huisken}. We will also study expansions of the Brown-York mass and the Hawking mass of geodesic spheres with center at a fixed point $p$ of a three manifold. Some geometric consequences will be derived.<br/>