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PreprintCC BY 4.0arXiv

Positive bisectional curvature, Ricci mass, and the fundamental group

  • Ved Datar
  • Vamsi Pritham Pingali
  • Harish Seshadri
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Abstract

We prove the finiteness of the integral of the top power of the Ricci form on a complete, noncompact Kähler manifold with positive bisectional curvature. This settles a special case of a conjecture of Yau and Yang. An immediate corollary is the finiteness of the fundamental group of such manifolds. As in our previous work, the main idea involves the construction and use of plurisubharmonic weight functions with finite Monge-Ampère masses.

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Cite

BibTeXRIS
BibTeX
@misc{datar2026positive,
  title = {{Positive bisectional curvature, Ricci mass, and the fundamental group}},
  author = {Ved Datar and Vamsi Pritham Pingali and Harish Seshadri},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.09989},
  eprint = {2610.09989},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.09989},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Positive bisectional curvature, Ricci mass, and the fundamental group
AU  - Ved Datar
AU  - Vamsi Pritham Pingali
AU  - Harish Seshadri
PY  - 2026
DA  - 2026/10/07
PB  - arXiv
DO  - 10.48550/arxiv.2610.09989
UR  - https://arxiv.org/abs/2610.09989
AB  - We prove the finiteness of the integral of the top power of the Ricci form on a complete, noncompact Kähler manifold with positive bisectional curvature. This settles a special case of a conjecture of Yau and Yang. An immediate corollary is the finiteness of the fundamental group of such manifolds. As in our previous work, the main idea involves the construction and use of plurisubharmonic weight functions with finite Monge-Ampère masses.
ER  -