On the spectral gap for fixed membranes

Burgess Davis Statistics Department, Purdue University

TBD mathscidoc:1701.332952

Arkiv for Matematik, 39, (1), 65-74, 1999.9
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$D$.
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  title={On the spectral gap for fixed membranes},
  author={Burgess Davis},
  booktitle={Arkiv for Matematik},
Burgess Davis. On the spectral gap for fixed membranes. 1999. Vol. 39. In Arkiv for Matematik. pp.65-74. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203600687535761.
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