Related papers: On geometry behind Birkhoff theorem

Some conjectures and open problems in convex geometry are presented, and their physical origin, meaning, and importance, for quantum theory and generic statistical theories, are briefly discussed.

The purpose of this article is to give a proof of the Orbifold Theorem announced by Thurston in late 1981: If $O$ is a compact, connected, orientable, irreducible and topologically atoroidal 3-orbifold with non-empty ramification locus,…

Complete complex parabolic geometries (including projective connections and conformal connections) are flat and homogeneous. This is the first global theorem on parabolic geometries.

In this article we present pictorially the foundation of differential geometry which is a crucial tool for multiple areas of physics, notably general and special relativity, but also mechanics, thermodynamics and solving differential…

Reducing the NP-problems to the convex/linear analysis on the Birkhoff polytope.

Since the subject of noncommutative geometry is now entering maturity, we felt there is need for presentation of the material at an undergraduate course level. Our review is a zero order approximation to this project. Thus, the present…

Beyond normal surfaces there are several open questions concerning 2- dimensional spaces. We present some results and conjectures along this line.

Covering theory is an important tool in representation theory of algebras, however, the results and the proofs are scattered in the literature. We give an introduction to covering theory at a level as elementary as possible.

Finsler spacetime geometry is a canonical extension of Riemannian spacetime geometry. It is based on a general length measure for curves (which does not necessarily arise from a spacetime metric) and it is used as an effective description…

In this paper, we generalize the notions of numerical radius parallelism and numerical radius Birkhoff orthogonality, originally formulated for operators on Hilbert spaces, to operators on normed spaces. We then proceed to demonstrate their…

We characterize Birkhoff-James orthogonality of continuous vector-valued functions on a compact topological space. As an application of our investigation, Birkhoff-James orthogonality of real bilinear forms are studied. This allows us to…

We extend a recent result of Tim Austin (see arXiv:0905.0515) to the L^1 setting, thus providing a general version of the Birkhoff ergodic theorem for functions taking values in nonpositively curved spaces. In this setting, the notion of a…

We give a very simple proof of a strengthened version of Chernoff's Inequality. We derive the same conclusion from much weaker assumptions.

In this article, we prove a theorem comparing the dihedral angles of simplices in the hyperbolic, spherical and Euclidean geometries.

We give a concise proof of the fundamental theorem of smoothing theory in the special case when a smoothing exists.

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

We introduce the notion of generalized bialgebra, which includes the classical notion of bialgebra (Hopf algebra) and many others. We prove that, under some mild conditions, a connected generalized bialgebra is completely determined by its…

The fundamental theorem of affine geometry says that a self-bijection $f$ of a finite-dimensional affine space over a possibly skew field takes left affine subspaces to left affine subspaces of the same dimension, then $f$ of the expected…

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

An technically interesting proof of a known theorem.