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arXiv · 2609.39636

The exact number of nonconstant positive solutions to the planar isotropic $L_p$ dual Minkowski problem

Guanyu Tao
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Abstract

We determine the exact number, up to rotations, of nonconstant positive $C^2$ solutions to the planar isotropic $L_p$ dual Minkowski problem for every $(p, q) \in \mathbb{R}^2$. We obtain a new parametrization of the associated period integral, characterize the regions where the period is strictly increasing or strictly decreasing, and prove that in the remaining nonmonotone region it has a unique nondegenerate maximum. As a consequence, we have a complete classification.

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Guanyu Tao. 2026-09-30. The exact number of nonconstant positive solutions to the planar isotropic $L_p$ dual Minkowski problem. https://arxiv.org/abs/2609.39636

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