Related papers: Geometric De Giorgi Theory
We pursue a geometrical approach to gravitational lensing theory. We present a survey of the background theory of General Relativity, including particular properties of the Schwarzschild and Kerr solutions. Next we outline a proof of the…
Here (the last paper in a series of four) we end our presentation of the basics of a systematical approach to the differential geometry of a smooth manifold M (supporting a metric field g and a general connection del) which uses the…
We revisit a little known theorem due to Beltrami, through which the integration of the geodesic equations of a curved manifold is accomplished by a method which, even if inspired by the Hamilton-Jacobi method, is purely geometric. The…
The algebro-geometric approach for integrability of semi-Hamiltonian hydrodynamic type systems is presented. This method is significantly simplified for so-called symmetric hydrodynamic type systems. Plenty interesting and physically…
We present the geometric formulation of gravity based on the mathematical structure of a Lie Algebroid. We show that this framework provides the geometrical setting to describe the gauge propriety of gravity.
The geodesic deviation equation (`GDE') provides an elegant tool to investigate the timelike, null and spacelike structure of spacetime geometries. Here we employ the GDE to review these structures within the…
Geometric complexity theory (GCT) is an approach to the P vs. NP and related problems. This article gives its complexity theoretic overview without assuming any background in algebraic geometry or representation theory.
Our goal in the present paper is to give a new ergodic proof of a well-known Veech's result, build upon our previous works.
The derivation of the phase transition in the model of Ga\'zdzicki and Gorenstein is generalized and simplified by using a geometrical construction.
In this article, we present a geometrical proof of sum of $\cos n\varphi$ where $n$ goes from $1$ up to $m$. Although there exist some summation forms and the proofs are simple, they use complex numbers. Our proof comes from a geometrical…
The present work represents a step to deal with stellar structure using a pure geometric approach. A geometric field theory is used to construct a model for a spherically symmetric configuration. The model obtained can be considered as a…
We show that Cheeger deformations regularize $G$--invariant metrics in a very strong sense.
The goal of this note is to give an alternative proof of local H\"older continuity for functions in DeGiorgi classes based on an idea of Moser.
We previously extended the Marsden-Ratiu reduction theorem in Poisson geometry by means of graded geometry (see Part I of Arxiv:1009.0948) . In this note we provide the background material about graded geometry necessary for the proof.…
We describe a new approach to the notion of general hypergeometric functions
Using Gillet's technique of projective envelopes, we prove a homological descent theorem for the connective K-homology of schemes.
The aim of this note is to give a simpler proof of a result of Avsec, which states that $q$-Gaussian algebras have the complete metric approximation property.
In this paper, some of formulations of Hamilton-Jacobi equations for Hamiltonian system on Lie algebroids are given. Here we use the general properties of Lie algebroids to express and prove two geometric version of the Hamilton-Jacobi…
In this paper, we establish the De Giorgi-Nash-Moser theory for a wide class of nonlinear equations driven by nonlocal, possibly degenerate, integro-differential operators, with the fractional $p$-Laplacian operator in Grushin-type spaces…
Call a pure Hodge structure geometric if it is contained in the cohomology of a smooth complex projective variety. The main goal is to show that for any set of Hodge numbers (subject to the obvious constraints), there exists a geometric…