Related papers: Uniformization

We give a proof of the geometric fundamental lemma of Kottwitz. As explained by Laumon, this implies the fundamental lemma for the unitary groups.

An approach is shown that proves various theorems of plane geometry in an algorithmic manner. The approach affords transparent proofs of a generalization of the Theorem of Morley and other well known results by casting them in terms of…

We present a geometric proof for the duality theorem of linear programming. Besides being self-contained and simple, the present approach also provides a transparent way for understanding this fundamental result.

This paper contains a complete proof of a fundamental theorem on the normalizers of unipotent subgroups in semisimple algebraic groups.

A vector variational principle is proved.

We prove a filtered version of the Homotopy Transfer Theorem which gives an A-infinity algebra structure on any page of the spectral sequence associated to a filtered dg-algebra. We then develop various applications to the study of the…

Let $\mathfrak{g}$ be a Color Lie Algebra and $\mathcal{U}(\mathfrak{g})$ its the universal Enveloping Algebra. We define the notion of graded deformations and we give explicit graded deformations of the universal Enveloping Algebra of…

We introduce an asymmetric operator of generalised translation, define the generalised modulus of smoothness by its means, and obtain the direct and inverse theorems in approximation theory for it.

We prove some restriction theorems for flat homogeneous surfaces of codimension greater than one.

The parametrization theorem is derived in a flat nD pseudo-complex affine space. The pseudo-complex hyperbolic space accomodates n-number of uncompactified time-like extra dimensions with sugnature (s,r), where s and r are the numbers of…

In this paper, we prove some foundational results on the deformation theory of E-infinity ring spectra.

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.

In this paper we present a geometrical framework to study the uniformity of a composite material by means of double groupoid theory. The notions of vertical and horizontal uniformity are introduced, as well as other weaker ones that allows…

Let $\Omega \subset \mathbb{C}^n$ be a bounded domain and let $\mathcal{A} \subset \mathcal{C}(\bar{\Omega})$ be a uniform algebra generated by a set $F$ of holomorphic and pluriharmonic functions. Under natural assumptions on $\Omega$ and…

Using toric geometry we prove a B\'ezout type theorem for weighted projective spaces.

The measurable Riemann mapping theorem proved by Morrey and in some particular cases by Ahlfors, Lavrentiev and Vekua, says that any measurable almost complex structure on $\rd$ ($S^2$) with bounded dilatation is integrable: there is a…

In this note we give a detailed proof of a theorem of Aubin.

In this paper I present a kind of proof for classical Euclidean geometric problems which relies on both synthetic and analytic geometry. Using the elementary tools of polynomial algebra and multivariate calculus we manage to reduce the…

An technically interesting proof of a known theorem.

We present a generalization of the induced matching theorem and use it to prove a generalization of the algebraic stability theorem for $\mathbb{R}$-indexed pointwise finite-dimensional persistence modules. Via numerous examples, we show…