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Stability Results for the First Eigenvalue of the Laplacian on Domains in Space Forms by Andrés I Ávila is a Mathematics article available to read on EtoBox.

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We studied the two known works on stability for isoperimetric inequalities of the first eigenvalue of the Laplacian. The earliest work is due to A. Melas who proved the stability of the Faber-Krahn inequality: for a convex domain contained in n with λ close to λ, the first eigenvalue of the ball B of the same volume, the domain must be close to the ball B with respect to the Hausdorff distance. Later, Y. Xu studied the stability of the Szegö-Weinberger inequality for convex domains in n and n where n denotes hyperbolic space. Our work consists of extending A. Melas' result to the spaces of constant curvature 2 and 2 and Y. Xu's result to domains contained in the polar cap B π/4 in n .  2002 Elsevier Science (USA)

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Author

Andrés I Ávila

Publisher

Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0022-247X)

Published

2002

Language

EN

Field

Mathematics (Physical Sciences)