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Willmore type inequality using monotonicity formulas

Differential Geometry 2020-08-12 v2

Abstract

Simon type monotonicity formulas for the Willmore functional H2\int | \mathbf{H} |^2 in the hyperbolic space Hn\mathbb{H}^n and Sn\mathbb{S}^n are obtained. The formula gives a lower bound of ΣH2\int_{\Sigma} | \mathbf{H} |^2 where Σ2\Sigma^2 is any closed surface in Hn\mathbb{H}^n.

Cite

@article{arxiv.1811.05617,
  title  = {Willmore type inequality using monotonicity formulas},
  author = {Xiaoxiang Chai},
  journal= {arXiv preprint arXiv:1811.05617},
  year   = {2020}
}

Comments

Comments welcome, 9 pages

R2 v1 2026-06-23T05:14:48.667Z