An inverse spectral problem on surfaces
An inverse spectral problem on surfaces
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曲面上的反谱问题
DOI：
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发表时间：
2006
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通讯作者：
P. Castillon
中科院分区：
文献类型：
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作者：
P. Castillon
本文的目的是证明黎曼曲面上某些算子的正性如何给出关于曲面共形类型的信息(这里所考虑的算子的形式是$Delta+lambDamathcal{K}$，其中$Delta$是曲面的拉普拉斯函数，$mathcal{K}$是曲面的曲率，$lambda$是实数)。特别地，我们得到了一个定理“a la Huber”：在谱假设下，我们证明了该曲面与去除有限个点的Riemann曲面共形等价。这个问题起源于对稳定极小曲面的研究。
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 $Delta+lambdamathcal{K}$ 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 ``a 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