Related papers: Une demonstration du theoreme de recouvrement de s…

In this note, we combine ideas of several previous proofs in order to obtain a quite short proof of Gr\"otzsch theorem.

We give a proof of Brooks' theorem and its list coloring extension using the algebraic method of Alon and Tarsi; this also shows that the Brooks' theorem remains valid in a more general game coloring setting.

In this short paper we review and extract some features of the Fredholm Alternative problem .

This is an expository paper giving a proof of the existence and uniqueness of smooth structures (hence also PL structures) on topological surfaces. Most published proofs rely on the topological Schoenflies theorem, but here we use instead…

Based on various strategies, we obtain several simple proofs of the celebrated Sharkovsky cycle coexistence theorem.

A short and almost elementary proof of the Boros-F\"uredi-B\'ar\'any-Pach-Gromov theorem on the multiplicity of covering by simplices in $\mathbb R^d$ is given.

The aim of this short note is to present an elementary, self-contained, and direct proof for the classical Lebesgue decomposition theorem.

We prove the multiple cover formula conjecture for abelian surfaces for a large class of insertions, including all stationary invariants. The proof uses the reduced degeneration formula expressing the invariants in terms of the correlated…

I present a simple, elementary proof of Morley's theorem, highlighting the naturalness of this theorem.

In the present paper continuing our previous work we prove an extension theorem for matrices with entries in the algebra of bounded holomorphic functions defined on an unbranched covering of a Caratheodory hyperbolic Riemann surface of…

A proof of the Ending Laminations Theorem is given, using Teichmuller geodesics directly.

The paper offers versions of Hilbert's Irreducibility Theorem for the lifting of points in a cyclic subgroup of an algebraic group to a ramified cover. A version of Bertini Theorem in this context is also obtained.

Torelli's theorem is proven by the study of the convolution product of the intersection cohomology sheaf of the thetadivisor.

In this paper, we present a short proof of Halin's grid theorem.

We show that Isserlis' theorem follows as a corollary to the invariant tensor theorem for isotropic tensors.

We provide a new simple and transparent proof of the version of Kummer's test given in [Tong, J. (1994). Amer. Math. Monthly. 101(5): 450--452]. Our proof is based on an application of a Hardy--Littlewood Tauberian theorem.

We shall give, in an optimal form, a sufficient numerical condition for the finiteness of the fundamental group of the smooth locus of a normal K3 surface. We shall moreover prove that, if the normal K3 surface is elliptic and the above…

We obtain an explicit expression for the number of ramified coverings of the sphere by the torus with given ramification type for a small number of ramification points, and conjecture this to be true for an arbitrary number of ramification…

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…

This is an exposition of Gauss's proof of Descartes's rule of signs.