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Diameter estimate for planar $L_p$ dual Minkowski problem
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Proc. Amer. Math. Soc. 152 (2024), 3035-3049

DOI: https://doi.org/10.1090/proc/16464

Published electronically: May 22, 2024

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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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