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PreprintCC BY 4.0arXiv

Harmonic functions and comparsion geometry for noncompact 3-manifolds with nonnegative scalar curvature

  • Jiannan Chen
  • Haiping Fu
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Abstract

In this paper, we establish several sharp comparsion results for noncompact 3-manifolds with nonnegative scalar curvature and with a compact, connected boundary under a boundary mean curvature condition. Then we apply these gradient estimates to establish a Cohn-Vossen type bound for the average of the scalar curvature. This generalizes the work of Colding-Minicozzi \cite{Cold4} and Oronzio \cite{Oro2}.

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Cite

BibTeXRIS
BibTeX
@misc{chen2026harmonic,
  title = {{Harmonic functions and comparsion geometry for noncompact 3-manifolds with nonnegative scalar curvature}},
  author = {Jiannan Chen and Haiping Fu},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.11331},
  eprint = {2611.11331},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.11331},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Harmonic functions and comparsion geometry for noncompact 3-manifolds with nonnegative scalar curvature
AU  - Jiannan Chen
AU  - Haiping Fu
PY  - 2026
DA  - 2026/11/08
PB  - arXiv
DO  - 10.48550/arxiv.2611.11331
UR  - https://arxiv.org/abs/2611.11331
AB  - In this paper, we establish several sharp comparsion results for noncompact 3-manifolds with nonnegative scalar curvature and with a compact, connected boundary under a boundary mean curvature condition. Then we apply these gradient estimates to establish a Cohn-Vossen type bound for the average of the scalar curvature. This generalizes the work of Colding-Minicozzi \cite{Cold4} and Oronzio \cite{Oro2}.
ER  -