English

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

Metric Geometry 2025-11-18 v2

Abstract

In this paper, we study the LpL_p dual Minkowski problem for all q,pRq, 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 LpL_p Minkowski problem (q=nq = n), the LpL_p Aleksandrov problem (q=0q = 0), and the dual Minkowski problem (p=0p = 0).

Keywords

Cite

@article{arxiv.2507.13233,
  title  = {The $L_{p}$ Dual Minkowski Problem for Group-Invariant Convex Bodies},
  author = {Junjie Shan},
  journal= {arXiv preprint arXiv:2507.13233},
  year   = {2025}
}