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The $L_{p}$ dual Christoffel-Minkowski problem for $1<p<q\leq k+1$ with $1\leq k\leq n$

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arxiv 2504.04931 v2 pith:ZT3NSC2Y submitted 2025-04-07 math.AP math.DG

Carlos Cabezas-Moreno , Jinrong Hu This is my paper · ORCID
classification math.APmath.DG
keywords problemdualmeasureareachristoffel-minkowskichristoffel-minkowski-typeclassconvex
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abstract

In this paper, we investigate an $L_{p}$ Christoffel-Minkowski-type problem that prescribes a class of $L_p$ geometric measures, which are mixtures of the $k$-th area measure and the $q$-th dual curvature measure. By establishing a gradient estimate, we obtain the existence of an even, smooth, strictly convex solution to this problem for $1 < p < q \leq k + 1$, where $1 \leq k \leq n$ and $n \geq 1$.

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  1. Compactness of the $L_p$ dual Minkowski problem in $\mathbb{R}^3$

    math.AP 2025-05 conditional novelty 7.0 of 10

    For convex bodies in R^3, bounded L_p qth dual curvature with p in [0,1) and q>2+p forces a uniform diameter upper bound and volume lower bound.

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