Corpus ID: 237503349

A non-existence result for the $L_p$-Minkowski problem

@inproceedings{Saroglou2021ANR,
  title={A non-existence result for the \$L\_p\$-Minkowski problem},
  author={Christos Saroglou},
  year={2021}
}
We show that given a real number p < 1, a positive integer n and a proper subspace H of R, the measure on the Euclidean sphere S, which is concentrated in H and whose restriction to the class of Borel subsets of S ∩H equals the spherical Lebesgue measure on S ∩ H , is not the Lp-surface area measure of any convex body. This, in particular, disproves a conjecture from [Bianchi, Böröczky, Colesanti, Yang, The Lp-Minkowski problem for −n < p < 1, Adv. Math. (2019)]. 

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