The Openness Conjecture and Complex Brunn-Minkowski Inequalities
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Publication:2795626
DOI10.1007/978-3-319-20337-9_2zbMath1337.32001arXiv1405.0989OpenAlexW2962979178MaRDI QIDQ2795626
Publication date: 22 March 2016
Published in: Complex Geometry and Dynamics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1405.0989
Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces (32-02) Plurisubharmonic functions and generalizations (32U05)
Related Items (43)
The metric geometry of singularity types ⋮ Lelong number and the log canonical thresholds of plurisubharmonic functions on analytic subsets ⋮ Complex Brunn-Minkowski inequalities and their applications in geometry ⋮ Concavity of minimal \(L^2\) integrals related to multiplier ideal sheaves on weakly pseudoconvex Kähler manifolds ⋮ Themes on Non-analytic Singularities of Plurisubharmonic Functions ⋮ Injectivity Theorems with Multiplier Ideal Sheaves and Their Applications ⋮ A non-Archimedean Ohsawa-Takegoshi extension theorem ⋮ Measure preserving holomorphic vector fields, invariant anti-canonical divisors and Gibbs stability ⋮ \(L^2\) extensions with singular metrics on Kähler manifolds ⋮ Modules of Square Integrable Holomorphic Germs ⋮ A log Canonical Threshold Test ⋮ Convexity of the extended K-energy and the large time behavior of the weak Calabi flow ⋮ Siu's lemma, optimal \(L^2\) extension and applications to twisted pluricanonical sheaves ⋮ A Kollár-type vanishing theorem ⋮ CONCAVITY PROPERTY OF MINIMAL INTEGRALS WITH LEBESGUE MEASURABLE GAIN ⋮ A curvature formula associated to a family of pseudoconvex domains ⋮ Siu's lemma: generalizations and applications ⋮ Uniform support function of the weighted \(L^2\) integrations with optimal asymptoticity ⋮ Effectiveness of Demailly's strong openness conjecture and related problems ⋮ Concavity of minimal \(L^2\) Integrals related to multiplier ideal sheaves ⋮ Interpolation, Prekopa and Brunn-Minkowski for \(F\)-subharmonicity ⋮ Geodesic rays and Kähler–Ricci trajectories on Fano manifolds ⋮ Direct images, fields of Hilbert spaces, and geometric quantization ⋮ Recent results in several complex variables and complex geometry ⋮ Equivalence of plurisubharmonic singularities and Siu-type metrics ⋮ Basis divisors and balanced metrics ⋮ Variation of singular Kähler-Einstein metrics: positive Kodaira dimension ⋮ A global approximation result by Bert Alan Taylor and the strong openness conjecture in \({\mathbb {C}}^n\) ⋮ Log canonical thresholds and Monge-Ampère masses ⋮ Nonexistence of decreasing equisingular approximations with logarithmic poles ⋮ A variational approach to the Yau–Tian–Donaldson conjecture ⋮ Cauchy–Riemann meet Monge–Ampère ⋮ Estimates of level sets of holomorphic functions and applications to the weighted log canonical thresholds ⋮ Optimal \(L^2\) extension and Siu's lemma ⋮ Positivity of character subbundles and minimum principle for noncompact group actions ⋮ A Nadel vanishing theorem via injectivity theorems ⋮ Roles of plurisubharmonic functions ⋮ Boundary asymptotics of the relative Bergman kernel metric for curves ⋮ Stability of multiplier ideal sheaves ⋮ $$L^2$$ L 2 estimates for the $$\bar{\partial }$$ ∂ ¯ operator ⋮ New properties of multiplier submodule sheaves ⋮ \(L^2\) extension and effectiveness of strong openness property ⋮ Ensemble equivalence for mean field models and plurisubharmonicity
Cites Work
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- Singular Hermitian metrics on holomorphic vector bundles
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- On extensions of the Brunn-Minkowski and Prekopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation
- The partial Legendre transformation for plurisubharmonic functions
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- Curvature of vector bundles associated to holomorphic fibrations
- The weighted log canonical threshold
- Semi-continuity of complex singularity exponents and Kähler–Einstein metrics on Fano orbifolds
- Bergman Geodesics
- The Brunn-Minkowski inequality
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