A flow approach to the $L_{-2}$ Minkowski problem

Mohammad N. Ivaki

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arXiv · 1205.6455

A flow approach to the $L_{-2}$ Minkowski problem

Mohammad N. Ivaki

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Abstract

We prove that the set of smooth, $π$-periodic, positive functions on the unit circle for which the $L_{-2}$ Minkowski problem is solvable is dense in the set of all smooth, $π$-periodic, positive functions on the unit circle with respect to the $L^{\infty}$ norm. Furthermore, we obtain a necessary condition on the solvability of the even $ L_{-2}$ Minkowski problem. At the end, we prove uniqueness of the solutions up to an affine linear transformation.

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Mohammad N. Ivaki. 2014-02-25. A flow approach to the $L_{-2}$ Minkowski problem. https://arxiv.org/abs/1205.6455

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