Erratum to: Sharp upper bound for the first eigenvalue
نویسندگان
چکیده
منابع مشابه
A Sharp Upper Bound for the First Dirichlet Eigenvalue and the Growth of the Isoperimetric Constant of Convex Domains
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...
متن کاملSharp Upper Bound for the First Non-zero Neumann Eigenvalue for Bounded Domains in Rank-1 Symmetric Spaces
In this paper, we prove that for a bounded domain Ω in a rank-1 symmetric space, the first non-zero Neumann eigenvalue μ1(Ω) ≤ μ1(B(r1)) where B(r1) denotes the geodesic ball of radius r1 such that vol(Ω) = vol(B(r1)) and equality holds iff Ω = B(r1). This result generalises the works of Szego, Weinberger and Ashbaugh-Benguria for bounded domains in the spaces of constant curvature.
متن کاملA sharp upper bound for the first eigenvalue of the Laplacian of compact hypersurfaces in rank-1 symmetric spaces
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...
متن کاملAn Upper Bound on the First Zagreb Index in Trees
In this paper we give sharp upper bounds on the Zagreb indices and characterize all trees achieving equality in these bounds. Also, we give lower bound on first Zagreb coindex of trees.
متن کاملA sharp upper bound on the largest Laplacian eigenvalue of weighted graphs
We consider weighted graphs, where the edge weights are positive definite matrices. The Laplacian of the graph is defined in the usual way. We obtain an upper bound on the largest eigenvalue of the Laplacian and characterize graphs for which the bound is attained. The classical bound of Anderson and Morley, for the largest eigenvalue of the Laplacian of an unweighted graph follows as a special ...
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ژورنال
عنوان ژورنال: Geometriae Dedicata
سال: 2014
ISSN: 0046-5755,1572-9168
DOI: 10.1007/s10711-014-0023-y