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Topology/Geometry Seminar

Compactness theory for harmonic maps into locally CAT(1) spaces

Sajjad Lakzian, Fordham University

Location:  Hill 525
Date & time: Tuesday, 10 October 2017 at 3:30PM - 4:30PM

Abstract:  We determine the complete bubble tree picture for a sequence of harmonic maps, with uniform energy bounds, from a compact Riemann surface into a compact locally CAT(1) space. In the smooth setting, Parker established the bubble tree picture by exploiting now classical analytic results about harmonic maps. Our work demonstrates that these results can be reinterpreted geometrically. Indeed, in the absence of a PDE we prove analogous results by taking advantage of the local convexity properties of the target space. Included in this paper are an \(epsilon\)-regularity theorem, an energy gap theorem, and a removable singularity theorem for harmonic maps. We also prove an isoperimetric inequality for conformal harmonic maps with small image (i.e. minimal surfaces in the non-smooth setting).

This is a joint work with Christine Breiner.

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