In this paper we obtain a curvature estimate for embedded minimal surfaces in a three-dimensional manifold of positive Ricci curvature in terms of the geometry of the ambient manifold and the genus… Expand

The medial axis of a plane domain is dened to be the set of the centers of the maximal inscribed disks. It is essentially the cut loci of the inward unit normal bundle of the boundary. We prove that… Expand

This work presents a novel approach to the Pythagorean hodograph curves, based on Clifford algebra methods, that unifies all known incarnations of PH curves into a single coherent framework and discusses certain differential or algebraic geometric perspectives that arise from this new approach.Expand

On obtient une borne inferieure pour la premiere valeur propre d'une hypersurface orientable compacte plongee de facon minimale dans une variete orientable compacte a courbure de Ricci positive

We define the asymptotic Dirichlet problem and give a sufficient condition for solving it. This proves an existence of nontrivial bounded harmonic functions on certain classes of noncompact complete… Expand

Using the new spline, called the Minkowski Pythagorean hodograph curve which was recently introduced, the algorithm is based on the domain decomposition scheme which reduces a complicated domain into a union of simple subdomains each of which is very easy to handle.Expand

A new means to differentiate among the solutions, namely, the winding number of the closed loop formed by a union of the hodographs of the PH quintic and of the unique “ordinary” cubic interpolant is introduced.Expand

It is proved that the minimum degree of non-planar PH curves whose ERF is an rotation-minimizing frame is seven, and the Euler–Rodrigues frame is equivalent to the Frenet frame on cubic PH curves.Expand

The Gauss map of a spacelike constant mean curvature hypersurface of Minkowski space is a harmonic map to hyperbolic space. The properties of such hypersurfaces are interpreted in terms of the… Expand

The concept of monotonic fundamental domain is introduced as a device for detecting the correct topology of offsets as well as for stable numerical computation.Expand