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arXiv · 2506.14735

A Minkowski problem for $\alpha$-concave functions via optimal transport

Xiao Li·Nguyen Dac Khoi Nguyen·Deping Ye
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Abstract

The notions of the Euclidean surface area measure and the spherical surface area measure of $\alpha$-concave functions in $\mathbb{R}^n$, with $-\frac{1}{n}<\alpha<0$, are introduced via a first variation of the total mass functional with respect to the $\alpha$-sum operation. Subsequently, these notions are extended to those for $\alpha$-concave measures. We then study the Minkowski problem associated with the Euclidean surface area measures of $\alpha$-concave measures via optimal transport.

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Xiao Li, Nguyen Dac Khoi Nguyen, Deping Ye. 2025-06-17. A Minkowski problem for $\alpha$-concave functions via optimal transport. https://arxiv.org/abs/2506.14735

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