Optimal Eigenvalues for Some Laplacians and Schrödinger Operators Depending on Curvature
نویسندگان
چکیده
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. c ©1998 by the authors. Reproduction of this article, in its entirety, by any means is permitted for non–commercial purposes. ∗ Work supported by GA AS No.1048801 ∗∗ Work supported by N.S.F. grant DMS-9622730 + Work supported by N.S.F. grant DMS–9500840 1
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تاریخ انتشار 1998