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

Abdenago Barros G. Pacelli Bessa

Published 2004-10-22Version 1

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.