Inverse spectral positivity for surfaces

Details Inverse spectral positivity for surfaces Inverse spectral positivity for surfaces

2011-11-25

arxiv.org/abs/1111.5928v2

Mathematics

Differential Geometry

Scientific paper

Let $(M,g)$ be a complete non-compact Riemannian surface. We consider operators of the form $\Delta + aK - q$, where $\Delta$ is the non-negative Laplacian, $K$ the Gaussian curvature, $q$ a non-negative function, and $a$ a positive real number. We address the question "What conclusions on $(M,g)$ and $q$ can one draw from the fact that the operator $\Delta + aK - q$ is non-negative" and we improve earlier results in particular in the cases $a = \4$ and $a \in (0,\4)$.

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