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- W1764420717 abstract "Let $lambda _{k}(Omega )$ be the $k$th Dirichlet eigenvalue of a bounded domain $Omega$ in $mathbb {R}^{n}$. According to Weylâs asymptotic formula we have [ lambda _{k}(Omega )thicksim C_{n}(k/V(Omega ))^{2/n}.] The optimal in view of this asymptotic relation lower estimate for the sums $sum _{j=1}^{k}lambda _{j}(Omega )$ has been proven by P.Li and S.T.Yau (Comm. Math. Phys. 88 (1983), 309-318). Here we will improve this estimate by adding to its right-hand side a term of the order of $k$ that depends on the ratio of the volume to the moment of inertia of $Omega$." @default.
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- W1764420717 date "2002-09-25" @default.
- W1764420717 modified "2023-09-27" @default.
- W1764420717 title "A lower bound for sums of eigenvalues of the Laplacian" @default.
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- W1764420717 doi "https://doi.org/10.1090/s0002-9939-02-06834-x" @default.
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