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Thomas Wolff Memorial Lecture in Mathematics

Tuesday, May 10, 2016
4:00pm to 5:00pm
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Lecture 3: New Results on Bounded, Complete Minimal Surfaces
Peter Jones, Professor, Mathematics & Applied Math, Yale University,

Abstract: The first example of a bounded, complete minimal surface was given in the 1970's (PJ). Since then several new types of such surfaces have been shown to exist. I will discuss recent research (PJ) showing that there exists a new type of example, namely a complete, bounded Legendrian disk in C^3. This means there are two bounded holomorphic functions (F, G) on the unit disk such that (F(z), G(z),z) is a complete, bounded minimal surface, with the property that (setting H'(z) = F(z)G'(z)) H is also a bounded holomorphic function. The construction uses a modification of Uchiyama's method of decomposing BMO functions into u + H(v), where u and v are bounded functions. I will also discuss some open problems in this area.

For more information, please contact Mathematics Department by phone at 626-395-4335 or by email at [email protected] or visit 15th Annual Wolff Memorial Lecture.