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The exact number of nonconstant positive solutions to the planar isotropic Lp dual Minkowski problem
Abstract
We determine the exact number, up to rotations, of nonconstant positive C2 solutions to the planar isotropic Lp dual Minkowski problem for every (p, q) ∈ ℝ2. 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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BibTeX
@misc{tao2026exact,
title = {{The exact number of nonconstant positive solutions to the planar isotropic $L_p$ dual Minkowski problem}},
author = {Guanyu Tao},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.39636},
eprint = {2609.39636},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.39636},
}
RIS
TY - UNPB
TI - The exact number of nonconstant positive solutions to the planar isotropic L_p dual Minkowski problem
AU - Guanyu Tao
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.39636
UR - https://arxiv.org/abs/2609.39636
AB - 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) ∈ 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.
ER -