Open AccessBook
Geometric function theory
TLDR
In this article, the authors consider the problem of holomorphic functions of several variables in the entire n space and show that the zero set of an entire function is not discrete and therefore one has no analogue of a tool such as the canonical Weierstrass product.Abstract:
We consider the basic problems, notions and facts in the theory of entire functions of several variables, i. e. functions J(z) holomorphic in the entire n space 1 the zero set of an entire function is not discrete and therefore one has no analogue of a tool such as the canonical Weierstrass product, which is fundamental in the case n = 1. Second, for n> 1 there exist several different natural ways of exhausting the spaceread more
Citations
More filters
Book
Lectures on Mappings of Finite Distortion
Stanislav Hencl,Pekka Koskela +1 more
TL;DR: In this paper, the authors propose a homeomorphism of finite distortion for null sets and show the integrability of Jf and 1/Jf with respect to null sets.
Posted Content
Degenerate complex Monge-Amp\`ere equations over compact K\
Jean-Pierre Demailly,Nefton Pali +1 more
TL;DR: In this article, the existence and uniqueness of the solutions of degenerate complex Monge-Amp\´ere equations is proved. And the solution of these equations is precisely what is needed in order to construct K\"ahler-Einstein metrics over irreducible singular K\"AHler spaces with ample or trivial canonical sheaf and singular K''ahler eigenvectors.
Journal ArticleDOI
Equicontinuity of mappings quasiconformal in the mean
TL;DR: In this article, the authors proved equicontinuity and normality of families R of the so-called ring Q(x)homeomorphisms with integral constraints of the type Φ(Q(x)) dm (x) < ∞ in a domain D ⊂ R, n ≥ 2.
Journal ArticleDOI
Jacobians of Sobolev homeomorphisms
Stanislav Hencl,Jan Malý +1 more
TL;DR: In this article, it was shown that each homeomorphism f in the Sobolev space satisfies either Jf ≥ 0 a.e or Jf ≤ 0 a, i.e. if n = 2 or n = 3.
Journal ArticleDOI
On boundary behavior of generalized quasi-isometries
TL;DR: In this article, a series of criteria for continuous and homeomorphic extension to the boundary of the lower Q-homeomorphisms f between domains in $$\overline {{^n] = {^{^n}} \cup \{ \infty \},n \ge 2$$¯¯, under integral constraints of the type ∫ Φ(Q n−1(x))dm(x) < ∞ with a convex non-decreasing function Φ: [0,∞]→[0, ∞].
References
More filters
Book
Lectures on Mappings of Finite Distortion
Stanislav Hencl,Pekka Koskela +1 more
TL;DR: In this paper, the authors propose a homeomorphism of finite distortion for null sets and show the integrability of Jf and 1/Jf with respect to null sets.
Journal ArticleDOI
Degenerate complex Monge-Ampère equations over compact Kähler manifolds
Jean-Pierre Demailly,Nefton Pali +1 more
TL;DR: In this article, the existence and uniqueness of the solutions of degenerate complex Monge-Ampere equations are proved and the regularity of their regularity is investigated, and it is shown that these types of equations are precisely what is needed in order to construct singular Kahler-Einstein metrics over irreducible singular spaces with ample or trivial canonical sheaf and singular KE metrics over varieties of general type.
Journal ArticleDOI
Jacobians of Sobolev homeomorphisms
Stanislav Hencl,Jan Malý +1 more
TL;DR: In this article, it was shown that each homeomorphism f in the Sobolev space satisfies either Jf ≥ 0 a.e or Jf ≤ 0 a, i.e. if n = 2 or n = 3.
Journal ArticleDOI
Mappings of finite distortion: the degree of regularity
TL;DR: In this paper, the authors studied the self-improving integrability properties of finite distortion mappings and showed that there exist two universal constants c1(n),c2(n) with the following property: if f is a mapping in Wloc1,1(Ω,Rn), with |Df(x)|n⩽K(x)J(x,f) for a.e.
Journal ArticleDOI
On boundary behavior of generalized quasi-isometries
TL;DR: In this article, a series of criteria for continuous and homeomorphic extension to the boundary of the lower Q-homeomorphisms f between domains in $$\overline {{^n] = {^{^n}} \cup \{ \infty \},n \ge 2$$¯¯, under integral constraints of the type ∫ Φ(Q n−1(x))dm(x) < ∞ with a convex non-decreasing function Φ: [0,∞]→[0, ∞].