Abstract
If (M 2,g) is a surface with Riemannian metric, then a family of immersed curves C t | 0 ≤ t < T on M 2 evolves by Curve Shortening if where K g is the geodesic curvature, and v is a unit normal to the curve. Since K g v can be written as where s is arclength along C, (1) is essentially a parabolic equation, i.e. a nonlinear heat equation.
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© 1999 Springer Science+Business Media Dordrecht
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Angenent, S. (1999). Inflection Points, Extatic Points and Curve Shortening. In: Simó, C. (eds) Hamiltonian Systems with Three or More Degrees of Freedom. NATO ASI Series, vol 533. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4673-9_1
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DOI: https://doi.org/10.1007/978-94-011-4673-9_1
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