# 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} }

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 $\C^n$.

## 6 Citations

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. 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 $\mathcal{S}$

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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…

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. 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

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

### Entire functions arising from trees

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Given any infinite tree in the plane satisfying certain topological conditions, we construct an entire function f with only two critical values ±1 and no asymptotic values such that f−1([−1, 1]) is…

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