# Construction of complete embedded self-similar surfaces under mean curvature flow. Part II

@article{Nguyn2008ConstructionOC,
title={Construction of complete embedded self-similar surfaces under mean curvature flow. Part II},
author={Xu{\^a}n Hi{\^e}n Nguy{\^e}n},
year={2008},
volume={15},
pages={503-530}
}
• X. H. Nguyên
• Published 23 October 2006
• Mathematics
We carry out the first main step towards the construc- tion of new examples of complete embedded self-similar surfaces under mean curvature flow. An approximate solution is obtained by taking two known examples of self-similar surfaces and desin- gularizing 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… Expand
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