A sharp upper bound for the first Dirichlet eigenvalue of cone-like domains
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DOI: 10.1007/s00013-020-01499-4
Abstract: The aim of this paper is to give a complementary upper bound-type isoperimetric inequality for the fundamental Dirichlet eigenvalue of a bounded domain completely contained in a cone. This inequality is a counterpart to the… read more here.
Keywords: inequality; dirichlet eigenvalue; sharp upper; upper bound ... See more keywords
The sharp lower bound of the first Dirichlet eigenvalue for geodesic balls
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DOI: 10.1007/s00209-021-02859-8
Abstract: On complete noncompact Riemannian manifolds with non-negative Ricci curvature, Li-Schoen proved the uniform Poincaré inequality for any geodesic ball. In this note, we obtain the sharp lower bound of the first Dirichlet eigenvalue of such… read more here.
Keywords: dirichlet eigenvalue; bound first; first dirichlet; lower bound ... See more keywords