Construction of Complete Embedded Self-Similar Surfaces under Mean Curvature Flow. Part II

Details Construction of Complete Embedded Self-Similar Surfaces under Mean Curvature Flow. Part II Construction of Complete Embedded Self-Similar Surfaces under Mean Curvature Flow. Part II

2007-04-07

arxiv.org/abs/0704.0981v1

Comm. in Partial Differential Equations, volume 34, Issue 3 (2009), p 257-280

Mathematics

Differential Geometry

30 pages

Scientific paper

We study the Dirichlet problem associated to the equation for self-similar surfaces for graphs over the Euclidean plane with a disk removed. We show the existence of a solution provided the boundary conditions on the boundary circle are small enough and satisfy some symmetries. This is the second step towards the construction of new examples of complete embedded self similar surfaces under mean curvature flow.

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