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The dual Minkowski problem for positive indices

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arxiv 2502.18032 v3 pith:ZFFQAIWO submitted 2025-02-25 math.AP math.DG

classification math.APmath.DG
keywords dualalphadensityevenindicesmeasureminkowskipositive
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abstract

We derive the stability result of the dual curvature measure with near constant density in the even case. As an application, the existence and uniqueness of solutions to the even dual Minkowski problem for positive indices in $\mathbb{R}^{n+1}$ are obtained with $n\geq 1$, provided the density of the given measure is close to 1 in the $C^{\alpha}$ norm with $\alpha\in (0,1)$.

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Cited by 1 Pith paper

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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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