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The dual Minkowski problem for positive indices
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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 $\alpha\in (0,1)$.
Forward citations
Cited by 2 Pith papers
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Compactness of the $L_p$ dual Minkowski problem in $\mathbb{R}^3$
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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Uniqueness in the near isotropic Lp dual Minkowski problem
For -1<p<1 and q sufficiently close to n, the near-isotropic Lp dual Minkowski problem on the sphere has a unique solution, with a sharp C0 estimate; the even case covers -1<p<q<min{n,n+p}.
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