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Returning to the Janowski Subordination of the Derivative of the Holomorphic Function
AbstractWe find a sharp estimate for the pre-Schwarzian derivative on the class of holomorphic functions in the unit disk with derivatives...
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Codimension One Holomorphic Foliations
It is known that the space of holomorphic foliations Foliation on some compact holomorphic manifold is a union of algebraic spaces. Here we intend to...
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Holomorphic Correspondences
In this chapter we prove that if a proper holomorphic map between bounded domains in...
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Proper Holomorphic Map**s
In this chapter we extend the results of the previous chapters to proper holomorphic map**s. For this we introduce proper holomorphic...
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Holomorphic extension in holomorphic fiber bundles with (1, 0)-compactifiable fiber
We use the Leray spectral sequence for the sheaf cohomology groups with compact supports to obtain a vanishing result. The stalks of sheaves
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Holomorphic Manifolds Over Algebras
In this chapter, we give the fundamental notions and some theorems concerning holomorphic functions and holomorphic manifolds which will be needed...
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A New Plurisubharmonic Capacity and Functions Holomorphic Along Holomorphic Vector Fields
The main purpose of this article is to present a generalization of Forelli’s theorem for functions holomorphic along a suspension of integral curves...
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The Grunsky norm of univalent functions and abelian holomorphic differentials
We establish that Grunsky norm of any normalized univalent function on a quasidisk is completely determined by the squares of holomorphic abelian...
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Holomorphic Continuation of Functions along a Fixed Direction (Survey)
In this article, we give an overview of the most significant and important results on holomorphic extensions of functions along a fixed direction. We...
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Holomorphic Foliations: Singularities and Local Geometric Aspects
This text has been written with the aim of providing a fast introduction to the framework of holomorphic foliations with singularities. Our...
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Complete norm-preserving extensions of holomorphic functions
We show that for every connected analytic subvariety V there is a pseudoconvex set Ω such that every bounded matrix-valued holomorphic function on V ...
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Holomorphic projective connections on compact complex threefolds
We prove that a holomorphic projective connection on a complex projective threefold is either flat, or it is a translation invariant holomorphic...
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Continuous Extension of Holomorphic Map**s
In this chapter introduce the Kobayashi-Royden and other invariant metrics, and prove continuous extension to the boundary of proper holomorphic maps...
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Normal Holomorphic Map**s in Complex Space
We study normal holomorphic map**s on complex spaces and complex manifolds. Applications are provided.
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Sparsity for Holomorphic Functions
In Chap. 3 we introduced a concept of holomorphic extensions of countably-parametric families...
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Rigidity of holomorphic map**s from local and global viewpoints
We consider rigidity of holomorphic map**s from local and global viewpoints. For instance, we derive a generalization of the famous multi-point...
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The holomorphic d-scalar curvature on almost Hermitian manifolds
In this paper, we study the existence of conformal metrics with constant holomorphic d-scalar curvature and the prescribed holomorphic d-scalar...