JournalscmhVol. 81, No. 2pp. 271–286

An inverse spectral problem on surfaces

  • Philippe Castillon

    Université de Montpellier II, France
An inverse spectral problem on surfaces cover
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Abstract

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 Δ+λK\Delta+\lambda\mathcal{K} where Δ\Delta is the Laplacian of the surface, K\mathcal{K} is its curvature and λ\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.

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Philippe Castillon, An inverse spectral problem on surfaces. Comment. Math. Helv. 81 (2006), no. 2, pp. 271–286

DOI 10.4171/CMH/52