Charles Arnal

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20232026

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math.DG2024

The distance function to a finite set is a topological Morse function

Charles Arnal

In this short note, we show that the distance function to any finite set $X \subset R^{n}$ is a topological Morse function, regardless of whether $X$ is in general position.…

math.DG2023

Critical points of the distance function to a generic submanifold

Charles Arnal, David Cohen-Steiner, Vincent Divol

In general, the critical points of the distance function $d_{M}$ to a compact submanifold $M \subset R^{D}$ can be poorly behaved. In this article, we show…