15 Citations
Differentiable Distance Spaces
- Mathematics
- 2015
The distance function $${\varrho(p, q) ({\rm or} d(p, q))}$$ϱ(p,q)(ord(p,q)) of a distance space (general metric space) is not differentiable in general. We investigate such distance spaces over…
On projectively flat Finsler spaces
- Mathematics
- 2013
First we present a short overview of the long history of projectively flat Finsler spaces. We give a simple and quite elementary proof of the already known condition for the projective flatness, and…
On projectively flat Finsler spaces
- MathematicsActa Mathematica Hungarica
- 2013
First we present a short overview of the long history of projectively flat Finsler spaces. We give a simple and quite elementary proof of the already known condition for the projective flatness, and…
Finsler geometry in the tangent bundle
- Mathematics
- 2007
Linear and metrical connections of a Riemannian space, whose indicatrices are ellipsoids, are established in the tangent bundle. lndicatrices of Finsler spaces are smooth, starshaped and convex…
Approximating geodesics via random points
- MathematicsThe Annals of Applied Probability
- 2019
Given a `cost' functional $F$ on paths $\gamma$ in a domain $D\subset\mathbb{R}^d$, in the form $F(\gamma) = \int_0^1 f(\gamma(t),\dot\gamma(t))dt$, it is of interest to approximate its minimum cost…
Stability of the optimal values under small perturbations of the constraint set
- Mathematics
- 2019
This paper discusses a general and useful stability principle which, roughly speaking, says that given a uniformly continuous function defined on an arbitrary metric space, if the function is bounded…
Raychaudhuri equation and singularity theorems in Finsler spacetimes
- Mathematics
- 2015
The Raychaudhuri equation and its consequences for chronality are studied in the context of Finsler spacetimes. It is proved that the notable singularity theorems of Lorentzian geometry extend to the…
References
SHOWING 1-10 OF 10 REFERENCES
Point Finsler spaces with metrical linear connections
- Mathematics
- 2000
We present a geometric construction of and constructive investigations in Finsler spaces ˜ F n = (M; ˜ L) whose indicatrices ˜ I(x) are ane images of a single indicatrix: ˜ I(x) = (x)I0. These are…
A note on the Gauss-Bonnet theorem for Finsler spaces
- Mathematics
- 1996
Exactly fifty years ago, one of us gave a proof of the Gauss-Bonnet formula for Riemannian manifolds by the method of transgression ([Chl], [Ch2]), and introduced a 'total curvature' H whose…
On the foundations of calculus of variations
- Mathematics
- 1941
The subject of this paper will be variational problems fF(x, t)dt = min in parameter form with fixed endpoints. The existence of rectifiable minimizing arcs has been proved under exceedingly general…
The local triangle axiom in topology and domain theory
- Mathematics
- 2003
We introduce a general notion of distance in weakly separated topological spaces. Our approach differs from existing ones since we do not assume the reflexivity axiom in general. We demonstrate that…
Handbook of the History of General Topology
- Mathematics
- 1997
Introduction. Combinatorial Topology Versus Point-set Topology I.M. James. Elements of the History of Locale Theory P. Johnstone. Nonsymmetric Distances and their Associated Topologies: About the…
Reelle Abstandsräume und hyperbolische Geometrie
- Mathematics
- 1998
AbstractEin reeller Abstandsraum ist eine Menge S ≠ ø zusammen mit einer Abbildung d: S × S → ℝ. Für x,y ∈ S hei\t d(x,y) der Abstand von x und y. Für beliebige reelle Abstandsräume definieren wir…
An Introduction to Riemann-Finsler Geometry
- Mathematics
- 2000
One Finsler Manifolds and Their Curvature.- 1 Finsler Manifolds and the Fundamentals of Minkowski Norms.- 1.0 Physical Motivations.- 1.1 Finsler Structures: Definitions and Conventions.- 1.2 Two…