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Nonlinear Analysis

Harmonic and biharmonic almost complex structures

Weiyong He, University of Oregon

Location:  Link: https://rutgers.zoom.us/meeting/register/tJ0vf-iqrD4qGtwChUSfeoQJj2JAiqpBekav Meeting ID: 992 8122 5008
Date & time: Wednesday, 14 October 2020 at 9:30AM - 10:30AM

Abstract: Harmonic almost complex structures was introduced by C. Wood in 1990s. We study the existence and regularity of weak harmonic almost complex structure from analytic point of view, as a tensor-valued version of harmonic maps. We also introduce the notion of biharmonic almost complex structures, in particular in dimension four. We prove that biharmonic almost complex structures are smooth, and there always exist an energy-minimizing biharmonic almost complex structure. Moreover, given a homotopy class, we also show existence results.

 We conjecture that the homotopy class of energy-minimizing biharmonic almost complex structures do not depend on a generic background metric.

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