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arXiv · 2507.13233

The $L_{p}$ Dual Minkowski Problem for Group-Invariant Convex Bodies

Junjie Shan
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Abstract

In this paper, we study the $L_p$ dual Minkowski problem for all $q, p \in \mathbb{R}$ from an algebraic perspective. We establish the existence of solutions for group-invariant convex bodies (not necessarily origin-symmetric), thereby covering three fundamental problems as special cases: the $L_p$ Minkowski problem ($q = n$), the $L_p$ Aleksandrov problem ($q = 0$), and the dual Minkowski problem ($p = 0$).

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Junjie Shan. 2025-07-17. The $L_{p}$ Dual Minkowski Problem for Group-Invariant Convex Bodies. https://arxiv.org/abs/2507.13233

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