Estimates of the first eigenvalue of minimal hypersurfaces of $\mathbb{S}^{n+1}$

Abdenago Barros; G. Pacelli Bessa

Estimates of the first eigenvalue of minimal hypersurfaces of $\mathbb{S}^{n+1}$

Differential Geometry 2016-08-04 v1 Analysis of PDEs

Authors: Abdenago Barros , G. Pacelli Bessa

Abstract

We consider a solution f of a certain Dirichlet Problem on a domain in $S^{(n+1)}$ whose boundary is a minimal hypersurface and we prove a Poincare type inequality for f. One have equality iff Yau's conjecture about the first non-zero eigenvalue of closed minimal hypersurfaces of $S^{(n+1)}$ is true.

Keywords

first eigenvalue minimal hypersurfaces dirichlet problem poincare inequality yau conjecture

Cite

@article{arxiv.math/0410493,
  title  = {Estimates of the first eigenvalue of minimal hypersurfaces of $\mathbb{S}^{n+1}$},
  author = {Abdenago Barros and G. Pacelli Bessa},
  journal= {arXiv preprint arXiv:math/0410493},
  year   = {2016}
}

Comments

A note of 5 pages

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