Related papers: Uniformization

In this paper, by combining techniques from Ricci flow and algebraic geometry, we prove the following generalization of the classical uniformization theorem of Riemann surfaces. Given a complete noncompact complex two dimensional K\"ahler…

Using theory of props we prove a formality theorem associated with universal quantizations of (strongly homotopy) Lie bialgebras.

This is mainly a small exposition on extensions of valuation rings as a filtered union of smooth algebras.

We give a conceptual explanation of universal deformation formulas for unital associative algebras and prove some results on the structure of their moduli spaces. We then generalize universal deformation formulas to other types of algebras…

We give a short proof of Ahlfors' theorem on covering surfaces.

We prove some symmetric $q$-congruences.

An algebraic deformation theory of dialgebra morphisms is obtained.

In this paper, for a given finitely generated algebra (an algebraic structure with arbitrary operations and no predicates) A we study finitely generated limit algebras of A, approaching them via model theory and algebraic geometry. Along…

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…

We introduce an elementary argument to the theory of distribution of sequences modulo one.

This is an elementary geometrical proof of Birkhoff theorem. It is hardly important, but the pictures behind are quite nice.

We prove completeness for the main examples of infinite-dimensional Lie groups and some related topological groups.

I give a proof of the uniform boundedness theorem that is elementary (i.e. does not use any version of the Baire category theorem) and also extremely simple.

We prove the splitting of the Kummer exact sequence and related exact sequences in arithmetic geometry.

We present an ongoing effort to implement Universal Algebra in the UniMath system. Our aim is to develop a general framework for formalizing and studying Universal Algebra in a proof assistant. By constituting a formal system for isolating…

We prove the following uniform version of a theorem by Lindstr\"om: Let $\mbox{$\cal F$}:=\{F_i:~ i\in I\}$ be a $k$-uniform set family of $[n]$, where $k\geq 1$. If $|\mbox{$\cal F$}|\geq n+1$, then there exist two disjoint subsets $I_1$…

A short proof of the Mazur-Ulam theorem concerning isometries of real normed spaces.

We prove an analogue in Arakelov geometry of the Grothendieck-Riemann-Roch theorem.

We prove a generalization of one of Lie's Theorems in the context of Lie-like algebras$^{2-nd}$.

We give a natural proof of the Ado theorem.