Compactness questions for triholomorphic maps

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• Costante Bellettini (DPMMS)
• Monday 12 October 2015, 15:00-16:00
• CMS, MR13.

If you have a question about this talk, please contact Amit Einav.

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 “almost hyper-Hermitian”: this more general setting leads to the weaker notion of”almost-stationarity”, without however affecting our compactness results and it leads e.g. to gauge-theoretic applications. This is a joint work with G. Tian (Princeton).

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

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