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The heat equation shrinking convex plane curves
Soient M et M' des varietes de Riemann et F:M→M' une application reguliere. Si M est une courbe convexe plongee dans le plan R 2 , l'equation de la chaleur contracte M a un point
Evolving Plane Curves by Curvature in Relative Geometries
In (0.1) X :S × [0, ω) → IR is the position vector of a family of closed convex plane curves, kN is the curvature vector, with k being the curvature and N the inward pointing normal given by N =
Curve shortening on surfaces
What happens when a simple closed curve on a surface M is allowed to move so that the instant instantaneous velocity at each point is proportional to the gepdesic curvature k of the curve at that
The Curve Shortening Flow
This is an expository paper describing the recent progress in the study of the curve shortening equation $${X_{{t\,}}} = \,kN $$ (0.1) Here X is an immersed curve in ℝ2, k the geodesic
A note on skew-Hopf fibrations
Each great circle fibration of the unit 3-sphere in 4-space can be identified with a subset of the Grassmann manifold of oriented 2-planes in 4-space by associating each great circle fiber with the