Related papers: Geometric De Giorgi Theory
The geodesic orbit property is useful and interesting in Riemannian geometry. It implies homogeneity and has important classes of Riemannian manifolds as special cases. Those classes include weakly symmetric Riemannian manifolds and…
In this paper, we study Noether gauge symmetries of geodesic motion for geodesic Lagrangian of four classes of metrics of G\"{o}del-type spacetimes for which we calculated the Noether gauge symmetries for all classes I-IV, and find the…
In this paper, we present a series of techniques to describe General Relativity using Geometric Algebra (GA). We emphasize the physical interpretation of quantities and provide a step-by-step guide for performing calculations. In doing so,…
In this article we obtain Holder estimates for solutions to second-order Hamilton-Jacobi equations with super-quadratic growth in the gradient and unbounded source term. The estimates are uniform with respect to the smallness of the…
We present a new geometric approach to the study of static isolated general relativistic systems for which we suggest the name geometrostatics. After describing the setup, we introduce localized formulas for the ADM-mass and ADM/CMC-center…
A geometric construction of Getzler's cohomological relation in the moduli space of 4 pointed elliptic curves is given by a push-forward of a natural rational equivalence in a space of admissible covers. In particular, Getzler's relation is…
A very short proof of Kneser's theorem via transversal is given.
We apply the Nash-Moser theorem for exact sequences of R. Hamilton to the context of deformations of Lie algebras and we discuss some aspects of the scope of this theorem in connection with the polynomial ideal associated to the variety of…
Let $(M,g)$ be a simple Riemannian manifold with boundary and consider the geodesic ray transform of symmetric 2-tensor fields. Let the integral of $f$ along maximal geodesics vanish on an appropriate open subset of the space of geodesics…
We give a geometric proof of a conjecture of W. Fulton on the multiplicities of irreducible representations in a tensor product of irreducible representations for GL(r).
The Hamilton-Jacobi theory is a formulation of Classical Mechanics equivalent to other formulations as Newton's equations, Lagrangian or Hamiltonian Mechanics. It is particulary useful for the identification of conserved quantities of a…
In a geometric unified theory there is an energy momentum equation, apart from the field equations and equations of motion. The general relativity Einstein equation with cosmological constant follows from this energy momentum equation for…
We develop a new approach to prove multiplier theorems in various geometric settings. The main idea is to use martingale transforms and a Gundy-Varopoulos representation for multipliers defined via a suitable extension procedure. Along the…
Coupling the Maxwell tensor to the Riemann-Christoffel curvature tensor is shown to lead to a geometricized theory of electrodynamics. While this geometricized theory leads directly to the classical Maxwell equations, it also extends their…
We study the behavior of the geodesics of strong Kropina spaces. The global and local aspects of geodesics theory are discussed. Our theory is illustrated with several examples.
Algorithms for the computation of geodesics on an ellipsoid of revolution are given. These provide accurate, robust, and fast solutions to the direct and inverse geodesic problems and they allow differential and integral properties of…
Motivated by the use of degenerate Jacobi metrics for the study of brake orbits and homoclinics, we develop a Morse theory for geodesics in conformal metrics having conformal factors vanishing on a regular hypersurface of a Riemannian…
Relationships that exist between the classical, Shannon-type, and geometric-based approaches to sampling are investigated. Some aspects of coding and communication through a Gaussian channel are considered. In particular, a constructive…
This book provides a self-contained introduction to geometric group theory. The topics range from an introduction of Cayley and Schreier graphs to Gromov's theorem on groups of polynomial growth and amenability. We discuss the ping-pong…
We prove descent theorems for semiorthogonal decompositions using techniques from derived algebraic geometry. Our methods allow us to capture more general filtrations of derived categories and even marked filtrations, where one descends not…