Stanford University

Tue 3 Mar 2015, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012

On the topology and index of minimal surfaces

ESB 2012
Tue 3 Mar 2015, 3:30pm4:30pm
Abstract
We show that for an immersed twosided minimal surface in R^3, there is a lower bound on the index depending on the genus and number of ends. Using this, we show the nonexistence of an embedded minimal surface in R^3 of index 2, as conjectured by Choe. Moreover, we show that the index of an immersed twosided minimal surface with embedded ends is bounded from above and below by a linear function of the total curvature of the surface. (This is joint work with Otis Chodosh)
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Korea Institute for Advanced Study

Tue 24 Mar 2015, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012

New characterizations of the catenoid and helicoid

ESB 2012
Tue 24 Mar 2015, 3:30pm4:30pm
Abstract
Bernstein and Breiner found a characterization of the catenoid that the area of a minimal annulus in a slab is bigger than that of the maximally stable catenoid in the same slab. We give a simpler proof of their theorem and extend the theorem to some minimal surfaces with genus (joint work with Benoit Daniel). New characterizations of the helicoid recently proved by Eunjoo Lee will be also presented.
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