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November 2018 Existence of solutions to the even dual Minkowski problem
Yiming Zhao
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J. Differential Geom. 110(3): 543-572 (November 2018). DOI: 10.4310/jdg/1542423629


Recently, Huang, Lutwak, Yang & Zhang discovered the duals of Federer’s curvature measures within the dual Brunn–Minkowski theory and stated the “Minkowski problem” associated with these new measures. As they showed, this dual Minkowski problem has as special cases the Aleksandrov problem (when the index is $0$) and the logarithmic Minkowski problem (when the index is the dimension of the ambient space)—two problems that were never imagined to be connected in any way. Huang, Lutwak, Yang & Zhang established sufficient conditions to guarantee existence of solution to the dual Minkowski problem in the even setting. In this work, existence of solution to the even dual Minkowski problem is established under new sufficiency conditions. It was recently shown by Böröczky, Henk & Pollehn that these new sufficiency conditions are also necessary.


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Yiming Zhao. "Existence of solutions to the even dual Minkowski problem." J. Differential Geom. 110 (3) 543 - 572, November 2018.


Received: 12 May 2016; Published: November 2018
First available in Project Euclid: 17 November 2018

zbMATH: 06982219
MathSciNet: MR3880233
Digital Object Identifier: 10.4310/jdg/1542423629

Primary: 35J20 , 52A38 , 52A40

Keywords: dual Brunn–Minkowski theory , dual curvature measures , dual Minkowski problem , Monge–Ampère equation

Rights: Copyright © 2018 Lehigh University


Vol.110 • No. 3 • November 2018
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