Related papers: Hypermaps and multiply quasiplatonic Riemann surfa…

We construct polylogarithms on families of pointed Riemann surfaces of any genus which describe monodromies of meromorphic connections with simple poles. Furthermore, we show that the polylogaritms are computable as power series in…

As a generalization of holomorphic submersions, anti-invariant submersions and slant submersions, we introduce slant Riemannian maps from almost Hermitian manifolds to Riemannian manifolds. We give examples, obtain the existence conditions…

We give the first part of a proof of Thurston's Ending Lamination conjecture. In this part we show how to construct from the end invariants of a Kleinian surface group a ``Lipschitz model'' for the thick part of the corresponding hyperbolic…

We give a complete classification of finite groups acting symplectically on supersingular K3 surfaces of Artin invariant one. Using work of Dolgachev and Keum, this provides the full classification of tame finite symplectic automorphism…

We prove the existence of stationary discs in the ball for small almost complex deformations of the standard structure. We define a local analogue of the Riemann map and establish its main properties. These constructions are applied to…

We introduce a systematic approach to express generating functions for the enumeration of maps on surfaces of high genus in terms of a single generating function relevant to planar surfaces. Central to this work is the comparison of two…

We gave an alternative short proof on the finite generation of holomorphic functions with polynomial growth on Riemann surfaces with nonnegative curvature. The first proof was due to Li and Tam.

Minimal surfaces in the sub-Riemannian Heisenberg group can be constructed by means of a Riemannian approximation scheme, as limit of Riemannian minimal surfaces. We study the regularity of Lipschitz, non-characteristic minimal surfaces…

The group of automorphisms of the free group on two generators is known to act geometrically, in an essentially unique way, on a 2-dimensional CAT(0) space X. We prove that X contains precisely two Hamiltonian surfaces. By this we mean a…

We produce for each natural number $n \geq 3$ two 1--parameter families of Riemann surfaces admitting automorphism groups with two cyclic subgroups $H_{1}$ and $H_{2}$ of orden $2^{n}$, that are conjugate in the group of…

With the help of hyper-ideal circle pattern theory, we have developed a discrete version of the classical uniformization theorems for surfaces represented as finite branched covers over the Riemann sphere as well as compact polyhedral…

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…

We prove a suite of results classifying holomorphic maps between configuration spaces of Riemann surfaces; we consider both the ordered and unordered setting as well as the cases of genus zero, one, and at least two. We give a complete…

We show that every finite group occurs as the automorphism group of infinitely many finite (field) extensions of any given Hilbertian field. This extends and unifies previous results of M. Fried and Takahashi on the global field case.

In this paper, we develop a new method to classify abelian automorphism groups of hypersurfaces. We use this method to classify (Theorem 4.2) abelian groups that admit a liftable action on a smooth cubic fourfold. A parallel result (Theorem…

A class of surfaces-graphs in a Riemannian 3-space with a prescribed projection of one field of principal directions onto a surface $\Pi$ is considered. A problem of determination of such surfaces when both principal curvatures are given…

We prove that the Brauer group of the generic diagonal surface of arbitrary degree is trivial. The same method is applied to surfaces whose equation can be written as the sum of two bilinear forms. This uses a general criterion for the…

A simple surface amalgam is the union of a finite collection of surfaces with precisely one boundary component each and which have their boundary curves identified. We prove if two fundamental groups of simple surface amalgams act properly…

A detailed study is made of super elliptic curves, namely super Riemann surfaces of genus one considered as algebraic varieties, particularly their relation with their Picard groups. This is the simplest setting in which to study the…

Hyperelliptic mapping class groups are defined either as the centralizers of hyperelliptic involutions inside mapping class groups of oriented surfaces of finite type or as the inverse images of these centralizers by the natural…