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Sharp monotonicity for closed three-manifolds with positive scalar curvature
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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BibTeX
@misc{manea2026sharp,
title = {{Sharp monotonicity for closed three-manifolds with positive scalar curvature}},
author = {Cosmin Manea},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.29853},
eprint = {2608.29853},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29853},
}
RIS
TY - UNPB
TI - Sharp monotonicity for closed three-manifolds with positive scalar curvature
AU - Cosmin Manea
PY - 2026
DA - 2026/08/30
PB - arXiv
DO - 10.48550/arxiv.2608.29853
UR - https://arxiv.org/abs/2608.29853
AB - 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.
ER -