In this paper, we consider the problem of computing a shortest path of bounded curvature amidst obstacles in the plane. More precisely, given prescribed initial and nal conngurations (i.e. positions and orientations) and a set of obstacles in the plane, we want to compute a shortest C 1 path joining those two conngurations, avoiding the obstacles, and with the further constraint that, on each C...

We introduce a family of conditions on a simplicial complex that we call local klargeness (k ≥ 6 is an integer). They are simply stated, combinatorial and easily checkable. One of our themes is that local 6-largeness is a good analogue of the nonpositive curvature: locally 6-large spaces have many properties similar to nonpositively curved ones. However, local 6-largeness neither implies nor is...

This paper shows that the continuous shearlet transform, a novel directional multiscale transform recently introduced by the authors and their collaborators, provides a precise geometrical characterization for the boundary curves of very general planar regions. This study is motivated by imaging applications, where such boundary curves represent edges of images. The shearlet approach is able to...

Given the Finsler structure (M, F) on a manifold M, a Riemannian structure (M, h) and a linear connection on M are defined. They are obtained as the " average " of the Finsler structure and the Chern connection. This linear connection is the Levi-Civita connection of the Riemannian metric h. The relation between parallel transport of the Chern connection and the Levi-Civita connection of h are ...

Separating two or more aspects of an object via cutting was likely important factor in the origin and evolution flaked stone technology. In recent years experiments have demonstrated that several tool attributes can influence different kinds behaviour: slicing, cleaving, scraping, sawing, drilling, piercing abrading. Here we experimentally assessed role flake plan- profile-view gross-edge curva...

We show, using purely classical considerations and logical extrapolation of results belonging to point particle theories, that the metric background field in which a string propagates must satisfy an Einstein or an Einstein–like equation. Additionally, there emerge restrictions on the worldsheet curvature, which seems to act as a source for spacetime gravity, even in the absence of other matter...

It is well known that no non-trivial Killing vector field exists on a compact Riemannian manifold of negative Ricci curvature; analogously, no non-trivial harmonic one-form exists on a compact manifold of positive Ricci curvature. One can consider the following, more general, problem. By reducing the assumption on the Ricci curvature to one on the scalar curvature, such vanishing theorems canno...