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Finite volume quotients of bounded domains with piecewise smooth boundary

  • Xingsi Pu
  • Lang Wang
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Abstract

We prove that a bounded pseudoconvex domain with piecewise C2-smooth boundary which has a finite volume quotient for the complete Kähler-Einstein metric is biholomorphic to a product of complex unit balls. More generally, the same conclusion holds for a bounded domain possessing a boundary point satisfying Kodama's conditions (C.1)-(C.5), provided the quotient has finite volume for a complete Aut(D)-invariant Kähler metric. For piecewise Levi-flat boundary the product is a polydisk and in the smooth pseudoconvex case it is a single ball.

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Cite

BibTeXRIS
BibTeX
@misc{pu2026finite,
  title = {{Finite volume quotients of bounded domains with piecewise smooth boundary}},
  author = {Xingsi Pu and Lang Wang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.19807},
  eprint = {2610.19807},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.19807},
}
RIS
TY  - UNPB
TI  - Finite volume quotients of bounded domains with piecewise smooth boundary
AU  - Xingsi Pu
AU  - Lang Wang
PY  - 2026
DA  - 2026/10/14
PB  - arXiv
DO  - 10.48550/arxiv.2610.19807
UR  - https://arxiv.org/abs/2610.19807
AB  - We prove that a bounded pseudoconvex domain with piecewise C^2-smooth boundary which has a finite volume quotient for the complete Kähler-Einstein metric is biholomorphic to a product of complex unit balls. More generally, the same conclusion holds for a bounded domain possessing a boundary point satisfying Kodama's conditions (C.1)-(C.5), provided the quotient has finite volume for a complete Aut(D)-invariant Kähler metric. For piecewise Levi-flat boundary the product is a polydisk and in the smooth pseudoconvex case it is a single ball.
ER  -