On the spectral gap for fixed membranes

Burgess Davis

doi:10.1007/BF02388791

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Home > Journals > Ark. Mat. > Volume 39 > Issue 1 > Article

March 2001 On the spectral gap for fixed membranes

Burgess Davis

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Burgess Davis¹
¹Statistics Department, Purdue University

Ark. Mat. 39(1): 65-74 (March 2001). DOI: 10.1007/BF02388791

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Abstract

The distance between the second and first eigenvalues for the Dirichlet Laplacian of a domain is called its (spectral) gap. We show that the gap of a convex planar domain D symmetric about both the x and y axes is no smaller than the gap of an oriented rectangle which contains D.