Positive Mass Theorem on manifolds admitting corners along a hypersurface

Pengzi Miao

doi:10.4310/ATMP.2002.v6.n6.a4

Positive Mass Theorem on manifolds admitting corners along a hypersurface

Pengzi Miao

Research output: Contribution to journal › Article › peer-review

86 Scopus citations

Abstract

We study a class of non-smooth asymptotically flat manifolds on which metrics fail to be C¹ across a hypersurface Σ. We first give an approximation scheme to mollify the metric, then we show that the Positive Mass Theorem [8] still holds on these manifolds if a geometric boundary condition is satisfied by metrics separated by Σ.

Original language	English (US)
Pages (from-to)	1163-1182
Number of pages	20
Journal	Advances in Theoretical and Mathematical Physics
Volume	6
Issue number	6
DOIs	https://doi.org/10.4310/ATMP.2002.v6.n6.a4
State	Published - Nov 2002
Externally published	Yes

ASJC Scopus subject areas

Mathematics(all)
Physics and Astronomy(all)

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abstract = "We study a class of non-smooth asymptotically flat manifolds on which metrics fail to be C1 across a hypersurface Σ. We first give an approximation scheme to mollify the metric, then we show that the Positive Mass Theorem [8] still holds on these manifolds if a geometric boundary condition is satisfied by metrics separated by Σ.",

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