Singular Kähler-Einstein metrics
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We study degenerate complex Monge-Ampère equations of the form ( ω + d d c φ ) n = e t φ μ (\omega +dd^c\varphi )^n = e^{t \varphi }\mu where ω \omega is a big semi-positive form on a compact Kähler manifold X X of dimension n n , t ∈ R + t \in \mathbb {R}^+ , and μ = f ω n \mu =f\omega ^n is a positive measure with density f ∈ L p ( X , ω n ) f\in L^p(X,\omega ^n) , p > 1 p>1 . We prove the existence and unicity of bounded ω \omega -plurisubharmonic solutions. We also prove that the solution is continuous under a further technical condition. In case X X is projective and ω = ψ
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Let X be a smooth projective variety of general type. Then X has a model with a Kähler-Einstein metric.
“(4) X has a model with a Kähler-Einstein metric.”
From Existence of minimal models for varieties of log general type (2009) · cites this paper as [4]
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Cited by
Sorted by citations
Existence of minimal models for varieties of log general type
Birkar, C., Cascini, P., Hacon, C., & McKernan, J. (2009) · Journal of the American Mathematical Society · doi:10.1090/s0894-0347-09-00649-3 · Cited by 1,278 · see citing works
- Authors
- Eyssidieux, P., Guedj, V., & Zeriahi, A.
- Affiliations
- Institut Fourier (FR)
- Institut de Mathématiques de Marseille (FR)
- ORCID
- Guedj, Vincent
- Venue
- Journal of the American Mathematical Society
- Publisher
- American Mathematical Society (AMS)
- Published
- 2009-02-06
- Volume
- 22
- Issue
- 3
- Pages
- 607-639
- ISSN
- 0894-0347 (ISSN-L)
- 1088-6834
- OpenAlex
- W2167259887
- Cited by
- 305
- References
- 49
- Citations by year
- 2026: 10 · 2025: 16 · 2024: 18 · 2023: 16 · 2022: 22 · 2021: 18 · 2020: 13 · 2019: 20 · 2018: 25 · 2017: 21 · 2016: 30 · 2015: 23 · 2014: 21 · 2013: 14 · 2012: 11
- FWCI
- 14.19
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- Locations
- Journal of the American Mathematical Society (publishedVersion, public-domain)
- arXiv (Cornell University) (submittedVersion)
- HAL (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Geometry and Topology › Geometry and complex manifolds
- Physical Sciences › Mathematics › Geometry and Topology › Algebraic Geometry and Number Theory
- Physical Sciences › Mathematics › Applied Mathematics › Nonlinear Partial Differential Equations
- Keywords
- compact Kähler manifolds, existence and uniqueness of solutions, continuity of solutions, projective manifolds
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