• Corpus ID: 16030301

Determining biholomorphic type of a manifold using combinatorial and algebraic structures

@article{Merenkov2013DeterminingBT,
  title={Determining biholomorphic type of a manifold using combinatorial and algebraic structures},
  author={Sergei Merenkov},
  journal={arXiv: Complex Variables},
  year={2013}
}
  • S. Merenkov
  • Published 22 May 2013
  • Mathematics
  • arXiv: Complex Variables
We settle two problems of reconstructing a biholomorphic type of a manifold. In the first problem we use graphs associated to Riemann surfaces of a particular class. In the second one we use the semigroup structure of analytic endomorphisms of domains in $\C^n$. 
View PDF on arXiv
6 Citations
Background Citations
1
Methods Citations
1

6 Citations

CONFORMAL AND CP TYPES OF SURFACES OF CLASS S

. In this paper we describe how to define the circle packing (cp) type (either cp parabolic or cp hyperbolic) of a Riemann surface of class S , and study the relation between this type and the…

Conformal and cp types of surfaces of class $\mathcal{S}$

In this paper we describe how to define the circle packing (cp) type(either cp parabolic or cp hyperbolic) of a Riemann surface of class $\mathcal{S}$, and study the relation between this type and…

Entire functions arising from trees

  • Weiwei Cui
  • Mathematics
    Science China Mathematics
  • 2021
Given any infinite tree in the plane satisfying certain topological conditions, we construct an entire function $f$ with only two critical values $\pm 1$ and no asymptotic values such that…

Iterated Monodromy Groups of Entire Maps and Dendroid Automata

. This paper discusses iterated monodromy groups for transcenden- tal functions. We show that for every post-singularly finite entire transcendental function, the iterated monodromy action can be…

Rapidly growing entire functions with three singular values

We settle the problem of finding an entire function with three singular values whose Nevanlinna characteristic dominates an arbitrarily prescribed function.

Chapter 18 – Quasiconformal Mappings in Value-Distribution Theory

References

SHOWING 1-10 OF 51 REFERENCES

Function theory of several complex variables

Some integral formulas. Subharmonicity and its applications. Convexity. Hormander's solution of the equation. Solution of the Levi problem and other applications of techniques. Cousin problems,…

On the characterization of a Riemann surface by its semigroup of endomorphisms

Suppose D 1 and D 2 be Riemann surfaces which have bounded nonconstant holomorphic functions. Denote by E(D i ), i = 1, 2, the semi-groups of all holomorphic endomorphisms. If φ: E(D 1 )→E(D 2 ) is…

Function theory in several complex variables

Fundamental theory: Holomorphic functions and domains of holomorphy Implicit functions and analytic sets The Poincare, Cousin, and Runge problems Pseudoconvex domains and pseudoconcave sets…

Hyperbolic complex spaces

1. Distance Geometry.- 2. Schwarz Lemma and Negative Curvature.- 3. Intrinsic Distances.- 4. Intrinsic Distances for Domains.- 5. Holomorphic Maps into Hyperbolic Spaces.- 6. Extension and Finiteness…

Covering properties of meromorphic functions, negative curvature and spherical geometry

Every nonconstant meromorphic function in the plane univalently covers spherical discs of radii arbitrarily close to arctan p 8… 70 ‐ 32 0 . If in addition all critical points of the function are…

Lectures on Riemann Surfaces

Contents: Covering Spaces.- Compact Riemann Surfaces.- Non-compact Riemann Surfaces.- Appendix.- References.- Symbol Index.- Author and Subject Index.

Uniformly hyperbolic surfaces

We prove the equivalence of certain uniform hyperbolicity conditions for open simply connected surfaces with non-positively curved intrinsic metric.

Functions conjugating entire functions toentire functions and semigroups of analytic endomorphisms

Answering two questions ot Rubei, we prove that there are unbounded plane domains which are notconformally or anticonformally equwalent but whose semigroups of analytic endomorphisms are isomorphic.…

Singular Surfaces and Meromorphic Functions

I n the nineteenth century the theory of analytic functions grew into a major field of mathematical research. Mostly, mathematicians were interested in properties of specific classes of analytic…

Random walk on the Speiser graph of a Riemann surface

On considere la determination du type conforme d'une surface de recouvrement de la sphere de Riemann a n points. On montre comment definir une marche aleatoire sur les sommets du graphe de Speiser de…
...