منابع مشابه
Curve Shortening and the Topology of Closed Geodesics on Surfaces
We study “flat knot types” of geodesics on compact surfaces M2. For every flat knot type and any Riemannian metric g we introduce a Conley index associated with the curve shortening flow on the space of immersed curves on M2. We conclude existence of closed geodesics with prescribed flat knot types, provided the associated Conley index is nontrivial.
متن کاملShortening Curves on Surfaces
METHODS of shortening a curve in a manifold have been used to establish the existence of closed geodesics, and in particular of simple closed geodesics on 2-spheres. For this purpose, a curve evolution process should (a) not increase the number of self-intersections of a curve, (b) exist for all time or until a curve collapses to a point, (c) shorten curves sufficiently fast so that curves whic...
متن کاملCurve Shortening and Grayson’s Theorem
In this chapter and the next we discuss the curve shortening flow (CSF). A number of important techniques in the field of geometric flows exhibit themselves in the curve shortening flow in an elegant and less technical way. The CSF was proposed in 1956 by Mullins to model the motion of idealized grain boundaries. In 1978 Brakke studied the mean curvature flow, of which the CSF is the 1-dimensio...
متن کاملIndirect illumination on curve surfaces
In this paper we suggest improved method of photon registration on curve surfaces, presented by triangulated mesh with “true” normals in mesh vertices. Such presentation is widely used for simulation the differing effects of light and color across the surface of an object (Phong shading). It was found that direct photon registration, which does not take into account interpolated (smooth) normal...
متن کاملInflection Points, Extatic Points and Curve Shortening
As the name suggests, Curve Shortening is a gradientflow for the length functional on the space of immersed curves in the surfaceM. One can therefore try to use Curve Shortening to prove existence of geodesics by variational methods. In my talk at S’Agarro I observed that geodesics always are curves without self-tangencies, and recalled that the space of such curves has many different connected...
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ژورنال
عنوان ژورنال: Annales scientifiques de l'École normale supérieure
سال: 1990
ISSN: 0012-9593,1873-2151
DOI: 10.24033/asens.1603