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arXiv · 2510.25968

Hadwiger's conjecture for cap bodies

Andrii Arman·Jaskaran Singh Kaire·Andriy Prymak
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Abstract

Hadwiger's covering conjecture states that every $n$-dimensional convex body can be covered by at most $2^n$ of its smaller positive homothetic translates, with $2^n$ copies required only for affine images of the $n$-cube. In this note, we confirm Hadwiger's conjecture for the class of cap bodies in all dimensions, bridging recently established cases of $n=3$ and large $n$. The proof uses probabilistic techniques and, for $4\le n \le 15$, computer-assisted linear programming.

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Andrii Arman, Jaskaran Singh Kaire, Andriy Prymak. 2025-10-29. Hadwiger's conjecture for cap bodies. https://arxiv.org/abs/2510.25968

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