English

Almost Monotonicity Formula for H-minimal Legendrian Surfaces in the Heisenberg Group

Differential Geometry 2023-02-06 v1

Abstract

We prove an almost monotonicity formula for H-minimal Legendrian Surfaces (also called {\it contact stationary legendrian immersions}) in the Heisenberg Group H2{\mathbb H}^2 . From this formula we deduce a Bernstein-Liouville type theorem for H-minimal Legendrian Surfaces. This last result happens to be in particular a central ingredient in the analysis part of the proof of the Willmore conjecture given by the author in arXiv:2007.05467

Keywords

Cite

@article{arxiv.2108.09685,
  title  = {Almost Monotonicity Formula for H-minimal Legendrian Surfaces in the Heisenberg Group},
  author = {Tristan Rivière},
  journal= {arXiv preprint arXiv:2108.09685},
  year   = {2023}
}