Positive Mass Theorem on Manifolds admitting Corners along a Hypersurface

Pengzi Miao

Positive Mass Theorem on Manifolds admitting Corners along a Hypersurface

Mathematical Physics 2016-09-07 v3 math.MP

Authors: Pengzi Miao

Abstract

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 $\Sigma$ .

Keywords

positive mass theorem asymptotically flat manifolds corners hypersurface metric approximation geometric boundary condition

Cite

@article{arxiv.math-ph/0212025,
  title  = {Positive Mass Theorem on Manifolds admitting Corners along a Hypersurface},
  author = {Pengzi Miao},
  journal= {arXiv preprint arXiv:math-ph/0212025},
  year   = {2016}
}

Comments

17 pages

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