Invariant surface area functionals and singular Yamabe problem in 3-dimensional CR geometry

Jih Hsin Cheng; Paul Yang; Yongbing Zhang

doi:10.1016/j.aim.2018.07.006

Invariant surface area functionals and singular Yamabe problem in 3-dimensional CR geometry

Jih Hsin Cheng, Paul Yang, Yongbing Zhang

Mathematics

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

3 Scopus citations

Abstract

We express two CR invariant surface area elements in terms of quantities in pseudohermitian geometry. We deduce the Euler–Lagrange equations of the associated energy functionals. Many solutions are given and discussed. In relation to the singular CR Yamabe problem, we show that one of the energy functionals appears as the coefficient (up to a constant multiple) of the log term in the associated volume renormalization.

Original language	English (US)
Pages (from-to)	405-465
Number of pages	61
Journal	Advances in Mathematics
Volume	335
DOIs	https://doi.org/10.1016/j.aim.2018.07.006
State	Published - Sep 7 2018

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

CR invariant surface area functional
Pseudohermitian geometry
Pseudohermitian torsion
Singular CR Yamabe problem
Tanaka–Webster curvature
Volume renormalization

Access to Document

10.1016/j.aim.2018.07.006

Cite this

@article{f9a5477c3be245e9803d501107cc4cac,

title = "Invariant surface area functionals and singular Yamabe problem in 3-dimensional CR geometry",

abstract = "We express two CR invariant surface area elements in terms of quantities in pseudohermitian geometry. We deduce the Euler–Lagrange equations of the associated energy functionals. Many solutions are given and discussed. In relation to the singular CR Yamabe problem, we show that one of the energy functionals appears as the coefficient (up to a constant multiple) of the log term in the associated volume renormalization.",

keywords = "CR invariant surface area functional, Pseudohermitian geometry, Pseudohermitian torsion, Singular CR Yamabe problem, Tanaka–Webster curvature, Volume renormalization",

author = "Cheng, {Jih Hsin} and Paul Yang and Yongbing Zhang",

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

year = "2018",

month = sep,

day = "7",

doi = "10.1016/j.aim.2018.07.006",

language = "English (US)",

volume = "335",

pages = "405--465",

journal = "Advances in Mathematics",

issn = "0001-8708",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - Invariant surface area functionals and singular Yamabe problem in 3-dimensional CR geometry

AU - Cheng, Jih Hsin

AU - Yang, Paul

AU - Zhang, Yongbing

PY - 2018/9/7

Y1 - 2018/9/7

N2 - We express two CR invariant surface area elements in terms of quantities in pseudohermitian geometry. We deduce the Euler–Lagrange equations of the associated energy functionals. Many solutions are given and discussed. In relation to the singular CR Yamabe problem, we show that one of the energy functionals appears as the coefficient (up to a constant multiple) of the log term in the associated volume renormalization.

AB - We express two CR invariant surface area elements in terms of quantities in pseudohermitian geometry. We deduce the Euler–Lagrange equations of the associated energy functionals. Many solutions are given and discussed. In relation to the singular CR Yamabe problem, we show that one of the energy functionals appears as the coefficient (up to a constant multiple) of the log term in the associated volume renormalization.

KW - CR invariant surface area functional

KW - Pseudohermitian geometry

KW - Pseudohermitian torsion

KW - Singular CR Yamabe problem

KW - Tanaka–Webster curvature

KW - Volume renormalization

UR - http://www.scopus.com/inward/record.url?scp=85049966658&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85049966658&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2018.07.006

DO - 10.1016/j.aim.2018.07.006

M3 - Article

AN - SCOPUS:85049966658

SN - 0001-8708

VL - 335

SP - 405

EP - 465

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

Invariant surface area functionals and singular Yamabe problem in 3-dimensional CR geometry

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

Other files and links

Fingerprint

Cite this