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arXiv · 2304.03478

Sobolev Inequalities in Spacelike Submanifolds of Minkowski Space

Liang Xu
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Abstract

We follow the method of ABP estimate in \cite{brendle2021} and apply it to spacelike submanifolds in $\mathbb R^{n,1}$. We then obtain Michael-Simon type inequalities. Surprisingly, our investigation leads to a Sobolev inequality without a mean curvature term, provided the hypersurface is mean convex.

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Liang Xu. 2023-04-07. Sobolev Inequalities in Spacelike Submanifolds of Minkowski Space. https://arxiv.org/abs/2304.03478

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