Positive Mass Theorem on Manifolds admitting Corners along a Hypersurface

By Pengzi Miao. 2002

235 citations recorded by the source corpus.

We study a class of non-smooth asymptotically flat manifolds on which metrics fails to be $C^1$ across a hypersurface $\Sigma$. We first give an approximation scheme to mollify the metric, then we prove that the Positive Mass Theorem still holds on these manifolds if a geometric boundary condition is satisfied by metrics separated by $\Sigma$.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5cadc9aa9e6a4b6aadb87b6cf0eb72aaa2a6ba9f

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In Applied Mathematics

1. M. Mars
2. Luen-Fai Tam
3. Yuguang Shi
4. Misha Gromov
5. Pengzi Miao
6. Lei Ni
7. A. Neves
8. Jintian Zhu

In Geometry and Topology

1. Luen-Fai Tam
2. Yuguang Shi
3. Misha Gromov
4. M. Mars
5. Assaf Naor
6. Yann Ollivier
7. Lei Ni
8. Alexander Lubotzky

In Mathematical Physics

1. M. Mars
2. Luen-Fai Tam
3. Yuguang Shi
4. Misha Gromov
5. Pengzi Miao
6. Assaf Naor
7. Yann Ollivier
8. A. Neves

Citations in the corpus

• Dirac and Plateau billiards in domains with corners (2014, background): “(a) The above style local “gluing + smoothing” appears in different forms in [2, 23, 38] and non-local smoothing with the Ricci flow is suggested in [37].”
• Present status of the Penrose inequality (2009, background): “This result, also due to Bray [22], has independent interest and has been already used in another context by P. Miao [117] to characterize the Schwarzschild initial data as the only static initial data with a non-empty minimal boundary.”
• Scalar curvature and singular metrics (2016, background): “3, then we still have positive mass for each end by the result in [21].”
• Positive Mass Theorem and the Boundary Behaviors of Compact Manifolds with Nonnegative Scalar Curvature (2002, methodology): “A similar result is still true in higher dimensions if we assume that each component Σi can be realized as a strictly convex hypersurface in the Euclidean space and if in addition Ω is spin.”
• On the volume functional of compact manifolds with boundary with constant scalar curvature (2008, background): “By the results in [19] again (see also [12]), we know that (Ω, g) is isometric to a domain in R.”