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arXiv · 2210.15646

Topology of singular set of semiconcave function via Arnaud's theorem

Tianqi Shi·Wei Cheng·Jiahui Hong
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Abstract

We proved the (local) path-connectedness of certain subset of the singular set of semiconcave functions with linear modulus in general. In some sense this result is optimal. The proof is based on a theorem by Marie-Claude Arnaud (M.-C. Arnaud, \textit{Pseudographs and the Lax-Oleinik semi-group: a geometric and dynamical interpretation}. Nonlinearity, \textbf{24}(1): 71-78, 2011.). We also gave a new proof of the theorem in time-dependent case.

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Tianqi Shi, Wei Cheng, Jiahui Hong. 2022-10-27. Topology of singular set of semiconcave function via Arnaud's theorem. https://arxiv.org/abs/2210.15646

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