Limits of epsilon-harmonic maps

Abstract: In 1981 Sacks and Uhlenbeck introduced their famous alpha-approximation of the Dirichlet energy for maps from surfaces and showed that critical points converge to a harmonic map (away from finitely many points). Now one can ask whether every harmonic map is captured by this limiting process. Lamm, Malchiodi and Micallef answered this for maps from the two sphere into the two sphere and showed that the Sacks-Uhlenbeck method produces only constant maps and rotations if the energy lies below a certain threshold. We investigate the same question for the epsilon-approximation of the Dirichlet energy. Joint work with Tobias Lamm and Mario Micallef.

differential geometry

Audience: researchers in the topic

B.O.W.L Geometry Seminar