Sharp estimate of global Coulomb gauge in dimension 4
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Title: Sharp estimate of global Coulomb gauge indimension 4
Speaker: Yu Wang (Northwestern University)
Time: 15:00 ―16:00, December13, 2018
Location: Room 200-9, Sir Shaw Run Run BusinessAdministration building,School of Mathematical Sciences, Yuquan Campus
Abstract: Considera principle SU(2)-bundle P over a compact 4-manifold M and a W^{1,2}-connectionA of P satisfying ||F_A||_{L^2}</infty. Our main result is the existence of a global section /sigma: M /to P with
controllably manysingularities such that the connection form /sigma*A satisfies the Coulombequation d*(/sigma* A) = 0 and moreover admits a sharp estimate.
In this talk, wefirst recall some preliminaries and then outlines the proof. If time allows we shallelaborate on the ideas to overcome the main difficulties in this problem, whichinclude an epsilon-regularity theorem for the Coulomb gauge, an annular-bubbleregions decomposition for the curvature, and studying the singularity behaviorof the Coulomb gauge on each annular and bubble region.
ContactPerson: Wenshuai Jiang (wsjiang@zju.edu.cn)