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Non-normalized solutions to the horospherical Minkowski problem
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abstract
Recently, the horospherical $p$-Minkowski problem in hyperbolic space was proposed as a counterpart of $L_p$ Minkowski problem in Euclidean space. Through designing a new volume preserving curvature flow, the existence of normalized even solution to the horospherical $p$-Minkowski problem was solved for all $p \in \mathbb{R}$. However, due to the lack of homogeneity of the horospherical $p$-surface area measure, it is difficult to remove the normalizing factor. In this paper, we overcome this difficulty for $-n\leq p<n$ by the degree-theoretic approach.
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Cited by 1 Pith paper
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The horospherical $p$-Christoffel-Minkowski and prescribed $p$-shifted Weingarten curvature problems in hyperbolic space
Smooth even strictly horospherically convex solutions exist for the horospherical p-Christoffel-Minkowski problem and the new p-shifted Weingarten problem in hyperbolic space for p≥−n, under convexity bounds on f.
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