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arXiv · 1611.01902

Scalar curvature rigidity and Ricci Deturck flow on perturbations of Euclidean Space

Alexander Appleton
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Abstract

We prove a rigidity result for non-negative scalar curvature perturbations of the Euclidean metric on $\mathbb{R^n}$ , which may be regarded as a weak version of the rigidity statement of the positive mass theorem. We prove our result by analyzing long time solutions of Ricci DeTurck flow. As a byproduct in doing so, we extend known $L^p$ bounds and decay rates for Ricci DeTurck flow and prove regularity of the flow at the initial data.

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Alexander Appleton. 2016-11-07. Scalar curvature rigidity and Ricci Deturck flow on perturbations of Euclidean Space. https://arxiv.org/abs/1611.01902

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