Related papers: A general model for time-minimizing navigation on …
We discuss the most general Finsler spacetime geometry obeying the cosmological symmetry group $\mathrm{SO}(4)$. On this background geometry we derive the equations of motion for the most general kinetic fluid obeying the same cosmological…
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…
The present paper studies globally defined Kropina metrics as solutions of the Zermelo's navigation problem. Moreover, we characterize the Kropina metrics of constant flag curvature showing that up to local isometry, there are only two…
In this paper, a descent method for nonsmooth multiobjective optimization problems on complete Riemannian manifolds is proposed. The objective functions are only assumed to be locally Lipschitz continuous instead of convexity used in…
The curvature discussed in this paper is a rather far going generalization of the Riemannian sectional curvature. We define it for a wide class of optimal control problems: a unified framework including geometric structures such as…
We develop a new Riemannian descent algorithm that relies on momentum to improve over existing first-order methods for geodesically convex optimization. In contrast, accelerated convergence rates proved in prior work have only been shown to…
We establish the existence of gravity water waves by applying a mountain pass theorem to a singular perturbation of the Alt-Caffarelli functional associated with the two-dimensional water wave equations. Our approach is formulated entirely…
We briefly review some basic concepts of parallel displacement in Finsler geometry. In general relativity, the parallel translation of objects along the congruence of the fundamental observer corresponds to the evolution in time. By…
Gravity is a phenomenon which arises due to the space-time geometry. The main equations that describe gravity are the Einstein equations. To understand the consequences of these field equations we need to calculate the free particle…
We present a phenomenological model for the nature in the Finsler and Randers space-time geometries. We show that the parity-odd light speed anisotropy perpendicular to the gravitational equipotential surfaces encodes the deviation from the…
We study the convergence of the Riemannian steepest descent algorithm on the Grassmann manifold for minimizing the block version of the Rayleigh quotient of a symmetric matrix. Even though this problem is non-convex in the Euclidean sense…
The generalized Finsler geometry, as well as Finsler geometry, is a generalization of Riemann geometry. The generalized Finsler geometry can be endowed with the Cartan connection. The generalized Finsler geometry and its Cartan connection…
In a previous study we investigated the spherically symmetric Schwarzschild and Schwarzschild-de Sitter solutions within a Finsler-Randers-type geometry. In this work we extend our analysis to charged and rotating solutions, focusing on the…
We present a new family of min-max optimization algorithms that automatically exploit the geometry of the gradient data observed at earlier iterations to perform more informative extra-gradient steps in later ones. Thanks to this adaptation…
In order to minimize a differentiable geodesically convex function, we study a second-order dynamical system on Riemannian manifolds with an asymptotically vanishing damping term of the form $\alpha/t$. For positive values of $\alpha$,…
This work is focused on searching a geodesic interpretation of the dynamics of a particle under the effects of a Snyder like deformation in the background of the Kepler problem. In order to accomplish that task, a newtonian spacetime is…
The incompatibility of explicit diffeomorphism violation with Riemannian geometry within the gravitational Standard-Model Extension (SME) is revisited. We review two methods of how to deal with this problem. The first is based on an…
Zermelo's navigation problem seeks the trajectory of minimal travel time between two points in a fluid flow. We address this problem for an agent -- such as a micro-robot or active particle -- that is advected by a two-dimensional flow,…
The specific astrophysical data collected during the last decade causes the need for the modification of the expression for the Einstein-Hilbert action, and several attempts sufficing this need are known. The modification suggested in this…
This paper proposes a generalized framework with joint normalization which learns lower-dimensional subspaces with maximum discriminative power by making use of the Riemannian geometry. In particular, we model the similarity/dissimilarity…