A potential theory for the k-curvature equation

Qiuyi Dai; Xu Jia Wang; Bin Zhou

doi:10.1016/j.aim.2015.11.003

A potential theory for the k-curvature equation

Qiuyi Dai, Xu Jia Wang, Bin Zhou^*

^*Corresponding author for this work

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

5 Citations (Scopus)

Abstract

In this paper, we introduce a potential theory for the k-curvature equation, which can also be seen as a PDE approach to curvature measures. We assign a measure to a bounded, upper semicontinuous function which is strictly subharmonic with respect to the k-curvature operator, and establish the weak continuity of the measure.

Original language	English
Pages (from-to)	791-824
Number of pages	34
Journal	Advances in Mathematics
Volume	288
DOIs	https://doi.org/10.1016/j.aim.2015.11.003
Publication status	Published - 22 Jan 2016

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title = "A potential theory for the k-curvature equation",

abstract = "In this paper, we introduce a potential theory for the k-curvature equation, which can also be seen as a PDE approach to curvature measures. We assign a measure to a bounded, upper semicontinuous function which is strictly subharmonic with respect to the k-curvature operator, and establish the weak continuity of the measure.",

keywords = "Curvature measure, Subharmonic functions, Weak continuity",

author = "Qiuyi Dai and Wang, \{Xu Jia\} and Bin Zhou",

note = "Publisher Copyright: {\textcopyright} 2015 Elsevier Inc.",

year = "2016",

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doi = "10.1016/j.aim.2015.11.003",

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T1 - A potential theory for the k-curvature equation

AU - Dai, Qiuyi

AU - Wang, Xu Jia

AU - Zhou, Bin

PY - 2016/1/22

Y1 - 2016/1/22

N2 - In this paper, we introduce a potential theory for the k-curvature equation, which can also be seen as a PDE approach to curvature measures. We assign a measure to a bounded, upper semicontinuous function which is strictly subharmonic with respect to the k-curvature operator, and establish the weak continuity of the measure.

AB - In this paper, we introduce a potential theory for the k-curvature equation, which can also be seen as a PDE approach to curvature measures. We assign a measure to a bounded, upper semicontinuous function which is strictly subharmonic with respect to the k-curvature operator, and establish the weak continuity of the measure.

KW - Curvature measure

KW - Subharmonic functions

KW - Weak continuity

UR - https://www.scopus.com/pages/publications/84947568600

U2 - 10.1016/j.aim.2015.11.003

DO - 10.1016/j.aim.2015.11.003

M3 - Article

SN - 0001-8708

VL - 288

SP - 791

EP - 824

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

A potential theory for the k-curvature equation

Abstract

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