GTA Seminar: Burns -- Holomorphic Extension and the Complex Monge-Ampère Equation

Speaker: Prof. Daniel Burns (University of Michigan, Ann Arbor)

http://www.math.lsa.umich.edu/people/facultyDetail.php?uniqname=dburns

Time: Tuesday, August 14, 12(NOON)--1PM

Room: AGR (Carslaw 829) 

Lunch: after the talk (at Taste at Sydney Uni, i.e. 
"Law School Annex Cafe")

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Title: Holomorphic Extension and the Complex Monge-Ampère
Equation 

Abstract: some time ago, Boutet de Monvel proved a Paley-Wiener 
type theorem for compact real analytic manifolds M, relating 
the exponential rate of convergence of the eigenfunction 
expansion of a real analytic function f with respect to an 
elliptic operator P with the radius of holomorphic extension 
of said function into the complex domain, i.e., into a 
neighborhood of M in its complexification. We discuss what 
happens when one wants to study this extension globally. 
This leads to holomorphic differential geometric properties 
of global complexifications, and especially exhaustions by 
solutions of the homogeneous complex Monge-Ampère equation. 
We also discuss another approach to these questions using 
the Toeplitz operators of Boutet de Monvel and Guillemin. 
This is joint work with Zhou Zhang and with Victor Guillemin.

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Web site for Geometry Seminar is at: 

http://www.maths.usyd.edu.au/u/SemConf/Geometry/index.html