Bottom spectrum and parabolicity of 3-manifolds with scalar curvature lower bound

Ovidiu Munteanu; Jiaping Wang

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arXiv · 2607.06508

Bottom spectrum and parabolicity of 3-manifolds with scalar curvature lower bound

Ovidiu Munteanu·Jiaping Wang

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Abstract

Under a necessary topological assumption, two global results are established for complete three dimensional manifolds. The first one provides a sharp upper bound for the bottom spectrum in terms of the scalar curvature lower bound. The second one shows that such manifolds do not admit any positive Green's function if the scalar curvature is bounded from below by a positive constant.

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Ovidiu Munteanu, Jiaping Wang. 2026-07-07. Bottom spectrum and parabolicity of 3-manifolds with scalar curvature lower bound. https://arxiv.org/abs/2607.06508

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