On the planar dual Minkowski problem

Shibing Chen; Qi Rui Li

doi:10.1016/j.aim.2018.05.010

On the planar dual Minkowski problem

Shibing Chen, Qi Rui Li^*

^*Corresponding author for this work

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

35 Citations (Scopus)

Abstract

In this paper, we resolve the planar dual Minkowski problem, proposed by Huang et al. (2016) [31] for all positive indices without any symmetry assumption. More precisely, given any q>0, and function f on S¹, bounded by two positive constants, we show that there exists a convex body Ω in the plane, containing the origin in its interior, whose dual curvature measure C˜_q(Ω,⋅) has density f. In particular, if f is smooth, then ∂Ω is also smooth.

Original language	English
Pages (from-to)	87-117
Number of pages	31
Journal	Advances in Mathematics
Volume	333
DOIs	https://doi.org/10.1016/j.aim.2018.05.010
Publication status	Published - 31 Jul 2018

Access to Document

10.1016/j.aim.2018.05.010

Cite this

@article{acd9e0f241ac46c385f593579f7ec76c,

title = "On the planar dual Minkowski problem",

abstract = "In this paper, we resolve the planar dual Minkowski problem, proposed by Huang et al. (2016) [31] for all positive indices without any symmetry assumption. More precisely, given any q>0, and function f on S1, bounded by two positive constants, we show that there exists a convex body Ω in the plane, containing the origin in its interior, whose dual curvature measure C˜q(Ω,⋅) has density f. In particular, if f is smooth, then ∂Ω is also smooth.",

keywords = "A priori estimates, Convex analysis, Degree theory, Dual Minkowski problem, Nonlinear equation",

author = "Shibing Chen and Li, {Qi Rui}",

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

year = "2018",

month = jul,

day = "31",

doi = "10.1016/j.aim.2018.05.010",

language = "English",

volume = "333",

pages = "87--117",

journal = "Advances in Mathematics",

issn = "0001-8708",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - On the planar dual Minkowski problem

AU - Chen, Shibing

AU - Li, Qi Rui

PY - 2018/7/31

Y1 - 2018/7/31

N2 - In this paper, we resolve the planar dual Minkowski problem, proposed by Huang et al. (2016) [31] for all positive indices without any symmetry assumption. More precisely, given any q>0, and function f on S1, bounded by two positive constants, we show that there exists a convex body Ω in the plane, containing the origin in its interior, whose dual curvature measure C˜q(Ω,⋅) has density f. In particular, if f is smooth, then ∂Ω is also smooth.

AB - In this paper, we resolve the planar dual Minkowski problem, proposed by Huang et al. (2016) [31] for all positive indices without any symmetry assumption. More precisely, given any q>0, and function f on S1, bounded by two positive constants, we show that there exists a convex body Ω in the plane, containing the origin in its interior, whose dual curvature measure C˜q(Ω,⋅) has density f. In particular, if f is smooth, then ∂Ω is also smooth.

KW - A priori estimates

KW - Convex analysis

KW - Degree theory

KW - Dual Minkowski problem

KW - Nonlinear equation

UR - http://www.scopus.com/inward/record.url?scp=85047524631&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2018.05.010

DO - 10.1016/j.aim.2018.05.010

M3 - Article

SN - 0001-8708

VL - 333

SP - 87

EP - 117

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

On the planar dual Minkowski problem

Abstract

Access to Document

Other files and links

Fingerprint

Cite this