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

General Mathematics

Access to Document

10.1016/j.aim.2018.10.032

Cite this

@article{b274129b6e4643bfb22506037645fb14,

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 = "Publisher Copyright: {\textcopyright} 2018 Elsevier Inc.",

year = "2019",

month = jan,

day = "7",

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

language = "English (US)",

volume = "341",

pages = "493--535",

journal = "Advances in Mathematics",

issn = "0001-8708",

publisher = "Academic Press Inc.",

}

TY - JOUR

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

AU - Bianchi, Gabriele

AU - Böröczky, Károly J.

AU - Colesanti, Andrea

AU - Yang, Deane

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

UR - http://www.scopus.com/inward/record.url?scp=85055997228&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85055997228&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2018.10.032

DO - 10.1016/j.aim.2018.10.032

M3 - Article

AN - SCOPUS:85055997228

SN - 0001-8708

VL - 341

SP - 493

EP - 535

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this

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

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this

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