The abstract presents a new theorem using Ross-Witt Nyström correspondence and Berndtsson's theorem.
problem The abstract tackles the Ohsawa-Takegoshi extension theorem and its applications.
method The approach uses Ross-Witt Nyström correspondence and Berndtsson's theorem in \(\mathbb{C}^*\)-degeneration.
result The approach provides a quick proof of the Ohsawa-Takegoshi extension theorem without limits or singular weights.
Paper generalizes complex Brunn-Minkowski theory and proves new extension theorems.
problem Complex Brunn-Minkowski theory and extension theorems.
method Hilbert bundle approach to complex Brunn-Minkowski theory.
result Generalizes Guan's sharp strong openness theorem and sharp Ohsawa-Takegoshi extension theorem.
Paper extends Ohsawa-Takegoshi theorem to more general domains, proving removable singularities for plurisubharmonic functions.
problem Removable singularities of plurisubharmonic functions on complex domains.
method Extending Ohsawa-Takegoshi L2 extension theorem to more general bounded complete Kähler domains. result Proves removable singularities for plurisubharmonic functions across compact complete pluripolar sets.
The paper proves extension theorems for holomorphic sections from divisors.
problem Extension of holomorphic sections from reduced unions of strata of divisors.
method Proves an Ohsawa--Takegoshi type extension theorem.
result Qualitative results on extension from snc divisors and generic global generation of vector bundles.
Using L2-methods for the ∂ˉ-equation we prove that the Ohsawa-Takegoshi extension theorem also holds for holomorphic sections of a vector bundle, over compact Kähler manifolds. We then proceed to show that the conditions that are needed are more liberal than the ones one would need if one instead reduced…
Study asymptotics of extension and orthogonal Bergman kernels for high tensor powers of positive line bundles.
problem Asymptotic behavior of Bergman kernels for high tensor powers of positive line bundles.
method Analyzing the Schwartz kernel of the Ohsawa-Takegoshi extension operator and orthogonal Bergman projector, proving exponential estimates and asymptotic expansions.
result Explicit asymptotic expansions for the Ohsawa-Takegoshi extension operator and orthogonal Bergman projector.
Paper proves integrability and entropy compactness for Kähler potentials with uniform log-log threshold.
problem Integrability and entropy compactness for Kähler potentials with specific density.
method Skoda-Zeriahi type integrability theorem and log-log threshold detection.
result Positivity of integrability threshold and entropy compactness for uniform log-log threshold.
Study optimal holomorphic extensions on complex manifolds with transitivity property.
problem Optimal holomorphic extensions on complex manifolds with transitivity property.
method Use Toeplitz operators and transitivity property for optimal holomorphic extensions.
result Transitivity property of optimal holomorphic extensions with small defect.
New extension theorem for projective manifolds.
problem Extension of twisted canonical forms on hypersurfaces.
method Established a new extension result for canonical forms on hypersurfaces with simple normal crossings.
result Obtained sharp bounds for the extension.
Study extends complex sections on non-holomorphic objects on Kähler manifolds.
problem Extension of smooth sections on non-holomorphic objects on Kähler manifolds.
method Use of asymptotically holomorphic line bundles, two twisted Laplace-type operators, and Bochner-Kodaira-Nakano-type inequalities.
result Extensions of smooth sections with control of their L2-norms for non-integrable objects. A new proof of an extension theorem with bounded generators.
problem Extension theorems in complex analysis.
method Skoda-type L2 division theorem with bounded generators. result The new division theorem allows α to be 1 in the norm of the datum. The paper defines positivity for singular metrics on vector bundles and proves related theorems.
problem Positivity of singular Hermitian metrics for holomorphic vector bundles.
method The method of Berndtsson and Lempert, along with a Berndtsson-type positivity theorem for holomorphic vector bundles.
result Sharp L2 extension theorem for holomorphic vector bundles. The paper characterizes curvature positivity and proves extension theorems for Kähler manifolds.
problem Characterizing and proving extension theorems for curvature positivity of differential forms.
method Introducing curvature operator \(A^E_{p,q}\), proving \(L^2\) extension theorem, and using twisted basic estimates.
result Proves \(L^2\) extension theorem and local freeness of higher direct image sheaves under curvature conditions.
The paper characterizes positivity of holomorphic vector bundles via Lp-estimates and extensions.
problem Characterizing positivity of holomorphic vector bundles using Lp-estimates and extensions. method Introducing four conditions for Hermitian (or Finsler) vector bundles and characterizing Nakano and Griffiths positivity.
result Characterization of Nakano and Griffiths positivity via specific Lp-conditions.