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On the Corona Problem for Strongly Pseudoconvex Domains
In this note we solve that the corona problem for strongly pseudoconvex domains under a certain assumption on the level sets of the corona data.
This...
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Parametrix for the localization of the Bergman metric on strictly pseudoconvex domains
We give the parameter version of a localization theorem for the Bergman metric near the boundary points of strictly pseudoconvex domains. The...
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Intrinsic derivative, curvature estimates and squeezing function
This survey paper consists of two folds. First of all, we recall the concept of intrinsic derivative which was introduced by Lu (1979) and the...
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q-subharmonicity and q-convex domains in ℂ n
In this paper we study q -subharmonic and q -plurisubharmonic functions in ℂ n . Next as an application, we give the notion of q -convex domains in ℂ ...
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Deformations of strongly pseudoconvex domains
We show that two smoothly bounded, strongly pseudoconvex domains which are diffeomorphic may be smoothly deformed into each other, with all...
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On the Gromov hyperbolicity of the Kobayashi metric on strictly pseudoconvex regions in the almost complex case
We prove that every bounded strictly J -convex region equipped with the Kobayashi metric is hyperbolic in the sense of Gromov. We give various...
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Stein Neighborhood Bases of Embedded Strongly Pseudoconvex Domains and Approximation of Map**s
In this paper we construct a Stein neighborhood basis for any compact subvariety A with strongly pseudoconvex boundary bA and Stein interior A ...
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The Bremermann–Dirichlet problem for unbounded domains of \({\mathbb{C}}^n\)
Given an unbounded strongly pseudoconvex domain Ω and a continuous real valued function h defined on b Ω , we study the existence of a (maximal)...
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Recent Results on the Extension Problem of Analytic Objects
We deal with the general problem of extension of analytic objects in a complex space X . After a short presentation of the classical results we...
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Convexity properties of coverings of 1-convex manifolds
We show the following result: let X be a 1-convex manifold, A its exceptional set, k = dim A and p : Y → X any covering. Then Y can be exhausted by an...
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Stein structures and holomorphic map**s
We prove that every continuous map from a Stein manifold X to a complex manifold Y can be made holomorphic by a homotopic deformation of both the map...
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On the -equation¶over pseudoconvex Kähler manifolds
The Picard variety Pic 0 (? n ) of a complex n -dimensional torus? n is the group of all holomorphic equivalence classes of topologically trivial...
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Theta-Functions and Modular Equations
Chapters 16–21 in his second notebook [22] contain much of Ramanujan’s prodigious outpouring of discoveries about theta-functions and modular...