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The space of minimal embeddings of a surface into a three-dimensional manifold of positive Ricci curvature
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 genusExpand
MATHEMATICAL THEORY OF MEDIAL AXIS TRANSFORM
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 thatExpand
Clifford Algebra, Spin Representation, and Rational Parameterization of Curves and Surfaces
TLDR
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
A first eigenvalue estimate for minimal hypersurfaces
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
ASYMPTOTIC DIRICHLET PROBLEMS FOR HARMONIC FUNCTIONS ON RIEMANNIAN MANIFOLDS
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 completeExpand
Medial axis transform and offset curves by Minkowski Pythagorean hodograph curves
TLDR
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
Construction and shape analysis of PH quintic Hermite interpolants
TLDR
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
Euler-Rodrigues frames on spatial Pythagorean-hodograph curves
  • H. Choi, C. Han
  • Mathematics, Computer Science
  • Comput. Aided Geom. Des.
  • 1 October 2002
TLDR
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
Gauss maps of spacelike constant mean curvature hypersurfaces of Minkowski space
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 theExpand
Two-dimensional offsets and medial axis transform
TLDR
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
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