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Transporting positive definiteness
This is a rough guide to the topic which might be worthy to develop further on. Expanding positive definiteness beyond its presupposed scope is...
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L2 Extension and Effectiveness of Lp Strong Openness Property
In this note, we present an L 2 extension approach to the effectiveness result of L p strong openness property of multiplier ideal sheaves.
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A Note on ξ-Bergman Kernels
In the present note, we introduce the ξ -complex singularity exponents, which come from the asymptotic property of ξ -Bergman kernels on sub-level sets...
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L2 Extension and Effectiveness of Strong Openness Property
In this note, we present an L 2 extension approach to the effectiveness result of strong openness property of multiplier ideal sheaves.
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L2 Extensions with Singular Metrics on Kähler Manifolds
In this paper, we give a survey of our recent results on extension theorems on Kähler manifolds for holomorphic sections or cohomology classes of...
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Convergence in Conformal Field Theory
Convergence and analytic extension are of fundamental importance in the mathematical construction and study of conformal field theory. The author...
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On an extrapolation problem for characteristic functions
Let f be the characteristic function of a probability measure μ f on ℝ n , and let σ > 0. We study the following extrapolation problem: under what...
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Concavity of minimal L2 integrals related to multiplier ideal sheaves on weakly pseudoconvex Kähler manifolds
In this paper, we present the concavity of the minimal L 2 integrals related to multiplier ideal sheaves on the weakly pseudoconvex Kähler manifolds...
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Optimal L2 Extension and Siu’s Lemma
In this paper, we discuss our most recent results on the optimal L 2 extension problem and Siu’s lemma as applications of the strong openness property...
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Regularization of quasi-plurisubharmonic functions on complex manifolds
In this paper, we give a survey of various regularization theorems of quasi-plurisubharmonic functions on complex manifolds, and we also discuss the...
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Strong openness of multiplier ideal sheaves and optimal L 2 extension
In this paper, we reveal that our solution of Demailly’s strong openness conjecture implies a matrix version of the conjecture; our solutions of two...
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Local Inverse Scattering
We develop a local version of the inverse scattering method for studying soliton equations of parabolic type (this includes, for example, Korteweg–de...
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A Lemma on Hartogs Function and Application to Levi Flat Hypersurfaces in Hopf Surfaces
The Levi form of the Hartogs function is computed for the domains with Levi flat boundary. The result is applied to the classification of Levi flat...
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Optimal constant in an L 2 extension problem and a proof of a conjecture of Ohsawa
In this paper, we solve the optimal constant problem in the setting of Ohsawa’s generalized L 2 extension theorem. As applications, we prove a...
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Complex Hulls of the Hyperboloid of One Sheet and Spherical Functions
For the hyperboloid of one sheet in \(\mathbb{R}^3\) ,...
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Holomorphic Extensions in Smooth Toric Surfaces
This article describes the Hartogs and the Hartogs–Bochner extension phenomena in smooth toric surfaces and the connection with the first cohomology...
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Extensions with estimates of cohomology classes
We prove an extension theorem of “Ohsawa-Takegoshi type” for Dolbeault q -classes of cohomology ( q ≥ 1) on smooth compact hypersurfaces in a weakly...
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Adapted complex structures and the geodesic flow
In this paper, we give a new construction of the adapted complex structure on a neighborhood of the zero section in the tangent bundle of a compact,...