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

Jih Hsin Cheng, Paul Chien-Ping Yang, Yongbing Zhang

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)405-465
Number of pages61
JournalAdvances in Mathematics
Volume335
DOIs
StatePublished - Sep 7 2018

Fingerprint

Yamabe Problem
Singular Problems
Surface area
Invariant
Euler-Lagrange Equations
Energy
Renormalization
Deduce
Express
Coefficient
Term

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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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.",
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Invariant surface area functionals and singular Yamabe problem in 3-dimensional CR geometry. / Cheng, Jih Hsin; Yang, Paul Chien-Ping; Zhang, Yongbing.

In: Advances in Mathematics, Vol. 335, 07.09.2018, p. 405-465.

Research output: Contribution to journalArticle

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