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

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 =… Expand

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… Expand

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… Expand

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… Expand