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Medientyp:
E-Artikel
Titel:
Singularities and Self Intersections of Curves Evolving on Surfaces
Beteiligte:
Oaks, Jeffrey A.
Erschienen:
Department of Mathematics INDIANA UNIVERSITY, 1994
Erschienen in:Indiana University Mathematics Journal
Sprache:
Englisch
ISSN:
0022-2518;
1943-5258
Entstehung:
Anmerkungen:
Beschreibung:
<p>It is proven that whenever a closed curve evolving by an arbitrary uniformly parabolic equation γt = V(T,k)N on a Riemannian manifold M develops a singularity, it either shrinks to a point or loses a self intersection. To aid in the calculations, it is first shown that locally it is enough to consider the ℝ2 case. Given a local conformal map from a neighborhood of M into another manifold M′ (which we later set to ℝ2), the image on M′ of γ also obeys an arbitrary uniformly parabolic equation.</p>