# 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}, journal={Advances in Differential Equations}, year={2008}, volume={15}, pages={503-530} }

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

#### 23 Citations

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The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Abstract. It has long been conjectured that starting at a generic smooth closed… Expand

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