FUNDAMENTAL TONE OF COMPLETE WEAKLY STABLE CONSTANT MEAN CURVATURE HYPERSURFACES IN HYPERBOLIC SPACE

Abstract

In this paper, we give an upper bound for the fundamental tone of stable constant mean curvature hypersurfaces in hyperbolic space. Let M be an n-dimensional complete non-compact constant mean curvature hypersurface with finite L2-norm of the If M is weakly stable, then traceless second fundamental form. λ1(M ) is bounded above by n2 + O(n2+s) for arbitrary s > 0.

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