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

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

2004-10-22

arxiv.org/abs/math/0410493v1

Matematica Conteporanea, vol 17, (1999) 71-75

Mathematics

Differential Geometry

A note of 5 pages

Scientific paper

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.

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