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arXiv · 2604.08285

Topology of 3-manifolds with nonnegative scalar curvature and positive harmonic functions

Zetian Yan·Xingyu Zhu
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Abstract

We study complete $3$-manifolds with nonnegative scalar curvature under additional regularity assumptions. We prove that a contractible such manifold is diffeomorphic to $\mathbb{R}^3$, and that an open handlebody admitting such a metric must have genus at most $1$. The proof uses exhaustions by level sets of harmonic functions and refined average gradient estimates.

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Zetian Yan, Xingyu Zhu. 2026-04-09. Topology of 3-manifolds with nonnegative scalar curvature and positive harmonic functions. https://arxiv.org/abs/2604.08285

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