A new proof of the bound for the first Dirichlet eigenvalue of the Laplacian operator

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Abstract

In this paper, we present a new proof of the upper and lower bound estimates for the first Dirichlet eigenvalue λ1D(B(p,r)) of Laplacian operator for the manifold with Ricci curvature Rc−K, by using Li-Yau’s gradient estimate for the heat equation.

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Analele Universitatii "Ovidius" Constanta - Seria Matematica

The Journal of "Ovidius" University of Constanta

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