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

N1 - Funding Information:
Acknowledgments. J.-H. Cheng would like to thank the Ministry of Science and Technology of Taiwan, R.O.C. for the support of the project: MOST 106-2115-M-001-013- and the National Center for Theoretical Sciences for the constant support. P. Yang would like to thank the NSF of the U.S. for the support of the grant: DMS 1509505. Y. Zhang would like to thank Professor Alice Chang for her invitation and the Department of Mathematics of Princeton University for its hospitality. He is supported by CSC scholarship 201606345025 and the Fundamental Research Funds for the Central Universities. P. Yang thanks Sean Curry for posing this question.
Funding Information:
Acknowledgments . J.-H. Cheng would like to thank the Ministry of Science and Technology of Taiwan , R.O.C. for the support of the project: MOST 106-2115-M-001-013- and the National Center for Theoretical Sciences for the constant support. P. Yang would like to thank the NSF of the U.S. for the support of the grant: DMS 1509505 . Y. Zhang would like to thank Professor Alice Chang for her invitation and the Department of Mathematics of Princeton University for its hospitality. He is supported by CSC scholarship 201606345025 and the Fundamental Research Funds for the Central Universities . P. Yang thanks Sean Curry for posing this question.
Publisher Copyright:
© 2018

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

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U2 - 10.1016/j.aim.2018.07.006

DO - 10.1016/j.aim.2018.07.006

M3 - Article

AN - SCOPUS:85049966658

VL - 335

SP - 405

EP - 465

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

ER -