A Variational Characterization of the Catenoid

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• Jacob Bernstein (Stanford)
• Monday 27 February 2012, 17:00-18:00
• CMS, MR15.

If you have a question about this talk, please contact Jonathan Ben-Artzi.

We show that the catenoid is the unique surface of least area (suitably understood) within a geometrically natural class of minimal surfaces. The proof relies on a techniques involving the Weierstrass representation used by Osserman and Schiffer to show the sharp isoperimetric inequality for minimal annuli. An alternate approach that avoids the Weierstrass representation will also be discussed. This latter approach depends on a conjectural sharp eigenvalue estimate for a geometric operater and has interesting connections with spectral theory. This is joint work with C. Breiner.

This talk is part of the Partial Differential Equations seminar series.

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