We consider total variation (TV) minimization for manifold-valued data. We propose a cyclic proximal point algorithm and a parallel proximal point algorithm to minimize TV functionals with -type data terms in the manifold case. These algorithms are based on iterative geodesic averaging which makes them easily applicable to a large class of data manifolds. As an application, we consider denoisin...

The aim of the present paper is to provide an intrinsic investigation of the fundamental properties of the most important geometric objects associated with the fundamental linear connections on a Finsler manifold. We introduce and investigate intrinsically the most general properties concerning the torsion tensor fields and the curvature tensor fields associated with a certain regular connectio...

We define a conformally invariant action S on gauge connections closed pseudo-Riemannian manifold M of dimension 6. At leading order this is quadratic in the connection. The Euler-Lagrange equations S, with respect to variation connection, provide higher-order analogue (source-free) Yang-Mills equations. For any connection A M, we S(A) by first defining Lagrangian density associated A. This not...

Abstract Using harmonic mean curvature flow, we establish a sharp Minkowski-type lower bound for total of convex surfaces with given area in Cartan-Hadamard $3$-manifolds. This inequality also improves the known estimates hyperbolic $3$-space. As an application, obtain Bonnesen-style isoperimetric distance function nonpositively curved $3$-spaces, via monotonicity results curvature. connection ...

The goal of this paper is to express the Bach tensor of a four– dimensional conformal geometry of an arbitrary signature by the Cartan normal conformal (CNC) connection. We show that the Bach tensor can be identified with the Yang–Mills current of the connection. It follows from that result that a conformal geometry whose CNC connection is reducible in an appropriate way has a degenerate Bach t...

In the present paper we construct differential invariants for generic rank 2 vector distributions on n-dimensional manifold. In the case n = 5 (the first case containing functional parameters) E. Cartan found in 1910 the covariant fourth-order tensor invariant for such distributions, using his ”reduction-prolongation” procedure (see [12]). After Cartan’s work the following questions remained op...

A rotating universe represented by the Gödel metric in spacetimes with Cartan torsion is investigated where the Cosmic Microwave Background Radiation (CMBR) is computed from the Gödel rotation of the universe and the spin density of the spinning fluid in EinsteinCartan gravity.The autoparallel equation in Riemann-Cartan spacetime is shown to lead to the evolution equation of the cosmological pe...

In this paper we will provide a new operatorial counterpart of the path-integral formalism of classical mechanics developed in recent years. We call it new because the Jacobi fields and forms will be realized via finite dimensional matrices. As a byproduct of this we will prove that all the operations of the Cartan calculus, such as the exterior derivative, the interior contraction with a vecto...