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arXiv · 2208.06284

Diameter estimate for planar $L_p$ dual Minkowski problem

Minhyun Kim·Taehun Lee
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Abstract

In this paper, given a prescribed measure on $\mathbb{S}^1$ whose density is bounded and positive, we establish a uniform diameter estimate for solutions to the planar $L_p$ dual Minkowski problem when $0<p<1$ and $q\ge 2$. We also prove the uniqueness and positivity of solutions to the $L_p$ Minkowski problem when the density of the measure is sufficiently close to a constant in $C^\alpha$.

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Minhyun Kim, Taehun Lee. 2022-08-12. Diameter estimate for planar $L_p$ dual Minkowski problem. https://doi.org/10.1090/proc/16464

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