Analysis Seminar

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Compactness Questions for Triholomorphic Maps

Speaker: Costante Bellettini

Location: Warren Weaver Hall 1302

Date: Thursday, September 17, 2015, 11 a.m.

Synopsis:

A triholomorphic map u between hyperKahler manifolds solves the "quaternion del-bar" equation du=I du i + J du j + K du k. Such a map turns out, under suitable assumptions, to be stationary harmonic. We focus on compactness issues regarding the quantization of the Dirichlet energy and the structure of the blow-up set. We can relax the assumptions on the manifolds, in particular we can take the domain to be merely "quaternion Kahler": this leads to the weaker notion of "almost-stationarity", without however affecting our compactness results. This is a joint work with G. Tian (Princeton).