Transactions of the American Mathematical Society

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

Author(s): Xuan Hien Nguyen
Journal: Trans. Amer. Math. Soc. 361 (2009), 1683-1701.
MSC (2000): Primary 53C44
Posted: November 25, 2008
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Abstract: We carry out the first main step towards the construction 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 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 self-similar surfaces. This provides us with an adequate central piece to substitute for the intersection.

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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 53C44

Xuan Hien Nguyen
Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
Address at time of publication: Department of Mathematics, Kansas State University, 138 Cardwell Hall, Manhattan, Kansas 66506

DOI: 10.1090/S0002-9947-08-04748-X
PII: S 0002-9947(08)04748-X
Keywords: Mean curvature flow, self-similar, singularities
Received by editor(s): September 13, 2006
Posted: November 25, 2008
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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