TRACE FORMULAS FOR S-1 INVARIANT GREENS OPERATORS ON S-2

Authors
ENGMAN M
Citation
M. Engman, TRACE FORMULAS FOR S-1 INVARIANT GREENS OPERATORS ON S-2, Manuscripta mathematica, 93(3), 1997, pp. 357-368
Citations number
9
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Manuscripta mathematica → ACNP
ISSN journal
00252611
Volume
93
Issue
3
Year of publication
1997
Pages
357 - 368
Database
ISI
SICI code
0025-2611(1997)93:3<357:TFFSIG>2.0.ZU;2-A
Abstract
We study the spectrum of the Laplacian acting on 1-forms for a surface of revolution diffeomorphic to S-2 and obtain, for the S-1 invariant spectrum, a trace formula for the eigenvalues of its Green's operator. The trace formula is used to ''hear'' negative curvature for some met rics and to prove the existence of metrics on S-2 with rather unusual spectral characteristics.