Construction of Complete Embedded SelfSimilar Surfaces under Mean Curvature Flow. Part I
Abstract
We carry out the first main step towards the construction of new examples of complete embedded selfsimilar surfaces under mean curvature flow. An approximate solution is obtained by taking two known examples of selfsimilar surfaces and desingularizing the intersection circle using an appropriately modified singly periodic Scherk surface, called the core. Using an inverse function theorem, we show that for small boundary conditions on the core, there is an embedded surface close to the core that is a solution of the equation for selfsimilar surfaces. This provides us with an adequate central piece to substitute for the intersection.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 October 2006
 arXiv:
 arXiv:math/0610695
 Bibcode:
 2006math.....10695H
 Keywords:

 Mathematics  Differential Geometry;
 53C44 (primary);
 35J65 (secondary)
 EPrint:
 24 pages, 3 pictures