### 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 | |

State | Published - Sep 7 2018 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Keywords

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

## Fingerprint Dive into the research topics of 'Invariant surface area functionals and singular Yamabe problem in 3-dimensional CR geometry'. Together they form a unique fingerprint.

## Cite this

Cheng, J. H., Yang, P., & Zhang, Y. (2018). Invariant surface area functionals and singular Yamabe problem in 3-dimensional CR geometry.

*Advances in Mathematics*,*335*, 405-465. https://doi.org/10.1016/j.aim.2018.07.006