The Lp-Minkowski problem for −n < p < 1

Gabriele Bianchi; Károly J. Böröczky; Andrea Colesanti; Deane Yang

doi:10.1016/j.aim.2018.10.032

The L_p-Minkowski problem for −n < p < 1

Gabriele Bianchi, Károly J. Böröczky, Andrea Colesanti, Deane Yang

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Chou and Wang's existence result for the L_p-Minkowski problem on Sⁿ⁻¹ for p∈(−n,1) and an absolutely continuous measure is discussed and extended to more general measures. In particular, we provide an almost optimal sufficient condition for the case p∈(0,1).

Original language	English (US)
Pages (from-to)	493-535
Number of pages	43
Journal	Advances in Mathematics
Volume	341
DOIs	https://doi.org/10.1016/j.aim.2018.10.032
State	Published - Jan 7 2019

Keywords

L Minkowski problem
Monge–Ampère equation

ASJC Scopus subject areas

Mathematics(all)

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title = "The Lp-Minkowski problem for −n < p < 1",

abstract = "Chou and Wang's existence result for the Lp-Minkowski problem on Sn−1 for p∈(−n,1) and an absolutely continuous measure is discussed and extended to more general measures. In particular, we provide an almost optimal sufficient condition for the case p∈(0,1).",

keywords = "L Minkowski problem, Monge–Amp{\`e}re equation",

author = "Gabriele Bianchi and B{\"o}r{\"o}czky, {K{\'a}roly J.} and Andrea Colesanti and Deane Yang",

note = "Funding Information: First and third authors are supported in part by the Gruppo Nazionale per l'Analisi Matematica, la Probabilit{\`a} e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM). Second author is supported in part by NKFIH grants 116451 , 121649 and 129630 . Publisher Copyright: {\textcopyright} 2018 Elsevier Inc.",

year = "2019",

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doi = "10.1016/j.aim.2018.10.032",

language = "English (US)",

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T1 - The Lp-Minkowski problem for −n < p < 1

AU - Bianchi, Gabriele

AU - Böröczky, Károly J.

AU - Colesanti, Andrea

AU - Yang, Deane

N1 - Funding Information: First and third authors are supported in part by the Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM). Second author is supported in part by NKFIH grants 116451 , 121649 and 129630 . Publisher Copyright: © 2018 Elsevier Inc.

PY - 2019/1/7

Y1 - 2019/1/7

N2 - Chou and Wang's existence result for the Lp-Minkowski problem on Sn−1 for p∈(−n,1) and an absolutely continuous measure is discussed and extended to more general measures. In particular, we provide an almost optimal sufficient condition for the case p∈(0,1).

AB - Chou and Wang's existence result for the Lp-Minkowski problem on Sn−1 for p∈(−n,1) and an absolutely continuous measure is discussed and extended to more general measures. In particular, we provide an almost optimal sufficient condition for the case p∈(0,1).

KW - L Minkowski problem

KW - Monge–Ampère equation

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JF - Advances in Mathematics

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