Sharp monotonicity for closed three-manifolds with positive scalar curvature

Cosmin Manea

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arXiv · 2608.29853

Sharp monotonicity for closed three-manifolds with positive scalar curvature

Cosmin Manea

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Abstract

We prove two sharp monotonicity formulae for the natural Green's function of a closed three-manifold with positive scalar curvature, analogous to the Munteanu-Wang theorem for non-negative scalar curvature. We also show that both results may be interpreted as the monotonicity of a suitably defined "enclosed mass" of the sublevel sets of Green's function in the corresponding "conformal" blow-up of the manifold.

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Cosmin Manea. 2026-08-30. Sharp monotonicity for closed three-manifolds with positive scalar curvature. https://arxiv.org/abs/2608.29853

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