A flow approach to the L_-2 Minkowski problem

2012/05/29 by Mohammad N. Ivaki, Ivaki, Mohammad N. · 1 citation
Mathematics · #52A10 #53A04 #53A15 (Primary) 35K55 (Secondary) #53C44 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #math.AP #math.DG #msc:35K55 #msc:52A10 #msc:53A04 #msc:53A15 #msc:53C44

paper · pdf · doi:10.48550/arxiv.1205.6455

to appear in Adv. Appl. Math, fixed some typos

arxiv created 2014/02/25 · arxiv updated 2014/02/27

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^∞ 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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