# The Role of Symmetry and Separation in Surface Evolution and Curve Shortening

@article{Broadbridge2011TheRO, title={The Role of Symmetry and Separation in Surface Evolution and Curve Shortening}, author={Philip Broadbridge and Peter J. Vassiliou}, journal={Symmetry Integrability and Geometry-methods and Applications}, year={2011}, volume={7}, pages={052} }

With few exceptions, known explicit solutions of the curve shortening flow (CSE) of a plane curve, can be constructed by classical Lie point symmetry reductions or by functional separation of variables. One of the functionally separated solutions is the exact curve shortening flow of a closed, convex \oval"-shaped curve and another is the smoothing of an initial periodic curve that is close to a square wave. The types of anisotropic evaporation coefficient are found for which the evaporation…

## 8 Citations

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With the help of heat equation, we first construct an example of a graphical solution to the curve shortening flow. This solution $ y\left(x, t\right) \ $has the interesting property that it…

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Curve shortening in the z-plane in which, at a given point on the curve, the normal velocity of the curve is equal to the curvature, is shown to satisfy StSz = Szz , where S(z, t) is the Schwarz…

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