Related papers: Une demonstration du theoreme de recouvrement de s…
We prove an analog of the classical Hartogs extension theorem for certain (possibly unbounded) domains on coverings of Stein manifolds.
We propose a simple proof of the vertical half-space theorem for Heisenberg space.
The main result of the paper is a boundedness for $n$-complements on algebraic surfaces. In addition, applications of this theorem to a classification of log Del Pezzo surfaces and of birational contractions for 3-folds are formulated.
A very short proof of G\"odel's second incompleteness theorem (for set theory, second order arithmetic etc.)
A proof is given of Rosenthal's \(\ell_1\) theorem.
We prove a better coloring theorem for aleph_4 and even aleph_3. This has a general topology consequence.
In this paper, we prove a conjecture of Schnell in the surface case.
We extend the well-known Denjoy-Ahlfors theorem on the number of different asymptotic tracts of holomorphic functions to subharmonic functions on arbitrary Riemannian manifolds. We obtain some new versions of the Liouville theorem for…
We give a proof for the fundamental theorem of algebra,using the Fredholm index phenomena
We will give a new proof for the Gromov's theorem on almost flat manifolds, which is an inductive proof on dimension.
We prove some restriction theorems for flat homogeneous surfaces of codimension greater than one.
We give a short proof of Waldhausen's homeomorphism theorem for orientable Haken 3-manifolds.
We give an elementary, self-contained and quick proof of Belyi's theorem. As a by-product of our proof we obtain an explicit bound for the degree of the defining number field of a Belyi surface.
In this paper, we show the abundance theorem for log canonical surfaces over fields of positive characteristic.
We present a simple proof of the surface classification theorem using normal curves. This proof is analogous to Kneser's and Milnor's proof of the existence and uniqueness of the prime decomposition of 3-manifolds. In particular, we do not…
We give a new proof of the fundamental theorem of algebra. It is entirely elementary, focused on using long division to its fullest extent. Further, the method quickly recovers a more general version of the theorem recently obtained by…
In this work, we prove a version of the fundamental theorem of submanifolds to target manifolds with warped structure.
We show that min-max minimal hypersurfaces can be localized. As a consequence, we obtain the sharp generalization to complete manifolds of the famous Almgren-Pitts min-max theorem in closed manifolds. We use this result to prove the…
In this note we provide a quick proof of the Sklar's Theorem on the existence of copulas by using the generalized inverse functions as in the one dimensional case, but a little more sophisticated.
A proof of the uniformization theorem of Riemann surface is given with only elementary properties of holomorphic functions and not using the paracompacity of the surface. This proof leans on an holomorphic version of the topological…