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

By X. H. Nguyen. Advances in Differential Equations, 2006

102 citations recorded by the source corpus.

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 core that is a solution of the equation for self-similar surfaces. This provides us with an adequate central piece to substitute for the intersection.

Subfields: Applied Mathematics, Mathematical Physics

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In Applied Mathematics

1. M. Li
2. N. Kapouleas
3. Marco A. M. Guaraco
4. Hung Tran
5. Peter J. McGrath
6. Xin Zhou
7. S. Brendle
8. Antoine Song

In Mathematical Physics

1. N. Kapouleas
2. M. Li

Citations in the corpus

• Free boundary minimal surfaces in the unit three-ball via desingularization of the critical catenoid and the equatorial disc (2017, methodology): “This is the case also for some recent desingularization constructions of self-shrinkers of the Mean Curvature Flow [44] [24] which are also based on [30].”