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Gluing constructions for minimal surfaces and self-shrinkers


Speaker: Nicolaos Kapouleas, Brown University
Location: 2112 MSB
Start time: Tue, Apr 10 2012, 3:10PM

In the first part of the talk I will discuss doubling constructions. In particular I will discuss in some detail a recent doubling construction for an equatorial two-sphere in the round three-sphere, and also potential generalizations for self-shrinkers of the Mean Curvature flow and doubling constructions in higher dimensions. In the second part of the talk I will briefly discuss the current understanding of desingularization constructions for minimal surfaces and self-shrinkers. In the third and final part I will discuss open uniqueness questions for closed embedded minimal surfaces in the round three-sphere inspired by the above constructions.