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Ricci entropy, RCD structures and Kahler spaces

  • Bin Guo
  • Jian Song
  • Jacob Sturm
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Abstract

This paper is the final installment in our series on the geometric theory of complex Monge-Ampere equations. We study singular Kahler metrics on compact normal Kahler spaces with klt singularities whose volume densities lie in Lp for some p>1. We show that a lower bound for the Ricci current in the sense of pluripotential theory is equivalent to a synthetic Ricci lower bound in the sense of RCD theory. As a consequence, every Kahler class on a compact normal Kahler space with klt singularities admits an RCD structure, which makes differential geometric analysis available on singular complex spaces. As an application, we show that the fundamental group of a compact Kahler Calabi-Yau space with klt singularities is almost Abelian. We further establish compactness results for singular Kahler-Einstein spaces.

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Cite

BibTeXRIS
BibTeX
@misc{guo2026ricci,
  title = {{Ricci entropy, RCD structures and Kahler spaces}},
  author = {Bin Guo and Jian Song and Jacob Sturm},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.28986},
  eprint = {2609.28986},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.28986},
}
RIS
TY  - UNPB
TI  - Ricci entropy, RCD structures and Kahler spaces
AU  - Bin Guo
AU  - Jian Song
AU  - Jacob Sturm
PY  - 2026
DA  - 2026/09/24
PB  - arXiv
DO  - 10.48550/arxiv.2609.28986
UR  - https://arxiv.org/abs/2609.28986
AB  - This paper is the final installment in our series on the geometric theory of complex Monge-Ampere equations. We study singular Kahler metrics on compact normal Kahler spaces with klt singularities whose volume densities lie in L^p for some p>1. We show that a lower bound for the Ricci current in the sense of pluripotential theory is equivalent to a synthetic Ricci lower bound in the sense of RCD theory. As a consequence, every Kahler class on a compact normal Kahler space with klt singularities admits an RCD structure, which makes differential geometric analysis available on singular complex spaces. As an application, we show that the fundamental group of a compact Kahler Calabi-Yau space with klt singularities is almost Abelian. We further establish compactness results for singular Kahler-Einstein spaces.
ER  -