An inverse spectral problem on surfaces

• Autores: Philippe Castillon
• Localización: Commentarii mathematici helvetici, ISSN 0010-2571, Vol. 81, Nº 2, 2006, págs. 271-286
• Idioma: inglés
• DOI: 10.4171/cmh/52
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• Resumen

  • 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