منابع مشابه
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We show that as the ratio between the first Dirichlet eigenvalues of a convex domain and of the ball with the same volume becomes large, the same must happen to the corresponding ratio of isoperimetric constants. The proof is based on the generalization to arbitrary dimensions of Pólya and Szegö’s 1951 upper bound for the first eigenvalue of the Dirichlet Laplacian on planar star-shaped domains...
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M |H| 2, where H is the mean curvature of the hypersurface M. These inequalities of Bleecker–Weiner and Reilly are also sharp for geodesic spheres in Rn. Since then, Reilly’s inequality has been extended to hypersurfaces in other simply connected space forms (see [7] and [8] for details and related results). While trying to understand these results, we noticed that one can obtain a similar shar...
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ژورنال
عنوان ژورنال: Geometriae Dedicata
سال: 2013
ISSN: 0046-5755,1572-9168
DOI: 10.1007/s10711-013-9863-0