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Uniqueness of solutions to a class of non-homogeneous curvature problems
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abstract
We show that the only even, smooth, convex solutions to a class of isotropic mixed Christoffel-Minkowski type problems are origin-centred spheres, which, in particular, answers a question of Firey 74 in the even isotropic case about kinematic measures. Employing the Heintze-Karcher inequality, we prove that the only smooth, strictly convex solutions to a large class of Minkowski type problems are origin-centred spheres. Immediate corollaries are the uniqueness of solutions to the isotropic Orlicz-Minkowski problem and the isotropic $L_p$-Gaussian-Minkowski problem when $p\geq 1$.
Forward citations
Cited by 2 Pith papers
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Weighted centro-affine Poincar\'e inequalities
Weighted centro-affine Poincaré inequalities yield L0 and Lp Brunn–Minkowski inequalities for dual quermassintegrals of unconditional convex bodies, with equality only for dilates.
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Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem
For -(n+1)<p<-1, isotropic Lp Gaussian Minkowski solutions with R(K)≤1 are unique and spherical, without assuming the body is origin-centered.
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