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Isoperimetric inequalities for eigenvalues of the Laplacian and the Schrödinger operator

Rafael D. Benguria, Helmut Linde, Benjamín Loewe

Bulletin of Mathematical Sciences · 2012 · 27 citations · 57 references

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Abstract

The purpose of this manuscript is to present a series of lecture notes on isoperimetric inequalities for the Laplacian, for the Schrödinger operator, and related problems.

References

57

Can One Hear the Shape of a Drum?

Mark Kac · American Mathematical Monthly · 1966 · 1.4K citations

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Curvature and the eigenvalues of the Laplacian

H. P. McKean, I. M. Singer · Journal of Differential Geometry · 1967 · 950 citations · Full text

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Can One Hear the Shape of a Drum?

Mark Kac · American Mathematical Monthly · 1966 · 779 citations

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The Brunn-Minkowski inequality in Gauss space

Christer Borell · Inventiones mathematicae · 1975 · 725 citations

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On extensions of the Brunn-Minkowski and Prékopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation

H. J. Brascamp, Élliott H. Lieb · Journal of Functional Analysis · 1976 · 672 citations

, , +10