Curve shortening on surfaces
@article{Gage1990CurveSO,
title={Curve shortening on surfaces},
author={Michael E. Gage},
journal={Annales Scientifiques De L Ecole Normale Superieure},
year={1990},
volume={23},
pages={229-256}
}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 point? This evolution is suggested by the equation of motion of an idealized elastic band along the surface (assuming that the friction term is relatively large and the mass relatively small)
51 Citations
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