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European Mathematical Society Publishing House
2016-09-19 17:04:51
Commentarii Mathematici Helvetici
Comment. Math. Helv.
CMH
0010-2571
1420-8946
General
10.4171/CMH
http://www.ems-ph.org/doi/10.4171/CMH
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European Mathematical Society Publishing House
Zuerich, Switzerland
© Swiss Mathematical Society
81
2006
2
An inverse spectral problem on surfaces
Philippe
Castillon
Université de Montpellier II, MONTPELLIER CEDEX 5, FRANCE
Spectral theory, minimal surfaces, stability operator
The purpose of this paper is to prove how the positivity of some operators on a Riemannian surface gives informations on the conformal type of the surface (the operators considered here are of the form $\Delta+\lambda\mathcal{K}$ where $\Delta$ is the Laplacian of the surface, $\mathcal{K}$ is its curvature and $\lambda$ is a real number). In particular we obtain a theorem ``à la Huber'': under a spectral hypothesis we prove that the surface is conformally equivalent to a Riemann surface with a finite number of points removed. This problem has its origin in the study of stable minimal surfaces.
Global analysis, analysis on manifolds
Differential geometry
General
271
286
10.4171/CMH/52
http://www.ems-ph.org/doi/10.4171/CMH/52