Optimal eigenvalues for some Laplacians and Schrödinger operators depending on curvature

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dc.creatorExner, Pavel
dc.creatorHarrell, Evans M.
dc.creatorLoss, Michael
dc.date1999-01-27
dc.date.accessioned2026-07-07T04:32:40Z
dc.date.available2026-07-07T04:32:40Z
dc.descriptionThis article is an expanded version of the plenary talk given by Evans Harrell at QMath98, a meeting in Prague, June 1998. We consider Laplace operators and Schrödinger operators with potentials containing curvature on certain regions of nontrivial topology, especially closed curves, annular domains, and shells. Dirichlet boundary conditions are imposed on any boundaries. Under suitable assumptions we prove that the fundamental eigenvalue is maximized when the geometry is round. We also comment on the use of coordinate transformations for these operators and mention some open problems.
dc.descriptionPlain TeX, 11 pages; to appear in the Proceedings of QMath7, Birkhäuser Verlag, Basel 1999
dc.identifierhttps://arxiv.org/abs/math-ph/9901022
dc.identifierhttp://arxiv.org/abs/math-ph/9901022
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/58276
dc.subjectMathematical Physics
dc.subjectQuantum Physics
dc.titleOptimal eigenvalues for some Laplacians and Schrödinger operators depending on curvature
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