Related papers: Sur la th\'eorie d'Ahlfors des surfaces

We give an elementary and self-contained proof of the uniformization theorem for non-compact simply-connected Riemann surfaces.

We show that various classical theorems of real/complex linear incidence geometry, such as the theorems of Pappus, Desargues, M\"obius, and so on, can be interpreted as special cases of a single "master theorem" that involves an arbitrary…

We present, discuss and generalize an elegant geometrical proof of the law of cosines, due to Al Cuoco.

We develop Nevanlinna's theory for a class of holomorphic maps when the source is a disc. Such maps appear in the theory of foliations by Riemann Surfaces.

We develop a gluing theory in the sense of Koll\'{a}r for slc surfaces and threefolds in positive characteristic. For surfaces we are able to deal with every positive characteristic $p$, while for threefolds we assume that $p>5$. Along the…

In this paper, we apply techniques from equivariant geometry to prove that a generalized Bour's theorem holds for surfaces that are invariant under the action of a one-parameter group of isometries of a three-dimensional Riemannian…

An algebraic deformation theory of coalgebra morphisms is constructed.

We extend the famous Erd\H{o}s-Szekeres theorem to $k$-flats in ${\mathbb{R}^d}$

We use the square peg problem for smooth curves to prove a generalized table Theorem for real valued functions on Riemannian surfaces with odd Euler characteristic. We then use this result to prove the table conjecture for even functions on…

The article introduces Ahlfors' generalization of the Schwarz lemma. With this powerful geometric tool of complex functions in one variable, we are able to prove some theorems concerning the size of images under holomorphic mappings,…

In this paper, we study the large-scale boundary regularity for the Stokes system in periodically oscillating John domains. Our main contribution is the construction of boundary layer correctors of arbitrary order. This is a significant…

We prove that, for translation surfaces whose homology is generated by the periodic orbits, the notions of - finite blocking property - pure periodicity - torus branched covering are equivalent. In particular, we prove this equivalence for…

The structure of the flow induced by the van der Waals destabilization of a non-wetting liquid film placed on a solid substrate is unraveled by means of theory and numerical simulations of the Stokes equations. Our analysis reveals that…

We show that using an idea from a paper by Van de Ven one may obtain a simple proof of Zak's classification of smooth projective surfaces with zero vanishing cycles. This method of proof allows one to extend Zak's theorem to the case of…

Many proofs of the Fundamental Theorem of Algebra, including various proofs based on the theory of analytic functions of a complex variable, are known. To the best of our knowledge, this proof is different from the existing ones.

We will give a new proof for the Gromov's theorem on almost flat manifolds, which is an inductive proof on dimension.

We prove a new cross theorem for separately holomorphic functions.

In this paper we lay the foundations of an $\infty$-categorical theory of Stokes data.

Theory of motivic superpolynomials is developed, including its extension to algebraic links colored by rows, relations to $L$-functions of plane curve singularities, the justification of the motivic versions of Weak Riemann Hypothesis, and…

We establish the reciprocity law along a vertical curve for residues of differential forms on arithmetic surfaces, and describe Grothendieck's trace map of the surface as a sum of residues. Points at infinity are then incorporated into the…