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arXiv · 2404.01962

Existence of solutions to the generalized dual Minkowski problem

Mingyang Li·Yannan Liu·Jian Lu
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Abstract

Given a real number $q$ and a star body in the $n$-dimensional Euclidean space, the generalized dual curvature measure of a convex body was introduced by Lutwak-Yang-Zhang [43]. The corresponding generalized dual Minkowski problem is studied in this paper. By using variational methods, we solve the generalized dual Minkowski problem for $q<0$, and the even generalized dual Minkowski problem for $0\leq q\leq1$. We also obtain a sufficient condition for the existence of solutions to the even generalized dual Minkowski problem for $1<q<n$.

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Mingyang Li, Yannan Liu, Jian Lu. 2024-04-02. Existence of solutions to the generalized dual Minkowski problem. https://arxiv.org/abs/2404.01962

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