Quasi-Local Mass Integrals and the Total Mass

作者: Pengzi Miao , Luen-Fai Tam , Naqing Xie

DOI: 10.1007/S12220-016-9721-Z

关键词: Reduced massMathematicsRiemann curvature tensorEinstein tensorRicci curvatureGeometryRicci decompositionMathematical physicsRicci flowScalar curvatureWeyl tensor

摘要: On asymptotically flat and hyperbolic manifolds, by evaluating the total mass via Ricci tensor, we show that limits of certain Brown–York type Hawking quasi-local integrals equal manifold in all dimensions.

参考文章(27)
André Neves, Insufficient convergence of inverse mean curvature flow on asymptotically hyperbolic manifolds Journal of Differential Geometry. ,vol. 84, pp. 191- 229 ,(2010) , 10.4310/JDG/1271271798
Xiaodong Wang, None, The Mass of Asymptotically Hyperbolic Manifolds Journal of Differential Geometry. ,vol. 57, pp. 273- 299 ,(2001) , 10.4310/JDG/1090348112
Yuguang Shi, Luen-Fai Tam, Positive Mass Theorem and the Boundary Behaviors of Compact Manifolds with Nonnegative Scalar Curvature Journal of Differential Geometry. ,vol. 62, pp. 79- 125 ,(2002) , 10.4310/JDG/1090425530
Lan-Hsuan Huang, On the center of mass in general relativity arXiv: Differential Geometry. ,(2011)
P T Chrusciel, A remark on the positive-energy theorem Classical and Quantum Gravity. ,vol. 3, pp. 1049- 1049 ,(1986) , 10.1088/0264-9381/3/6/002
Piotr T Chruściel, Marc Herzlich, None, The mass of asymptotically hyperbolic Riemannian manifolds Pacific Journal of Mathematics. ,vol. 212, pp. 231- 264 ,(2003) , 10.2140/PJM.2003.212.231
Louis Nirenberg, The Weyl and Minkowski problems in differential geometry in the large Communications on Pure and Applied Mathematics. ,vol. 6, pp. 337- 394 ,(1953) , 10.1002/CPA.3160060303
Ralph Howard, Blaschke's rolling theorem for manifolds¶with boundary Manuscripta Mathematica. ,vol. 99, pp. 471- 483 ,(1999) , 10.1007/S002290050186