Speaker: Andrew Lawrie (UC Berkeley)

Title: A refined threshold theorem for  $(1+2)$-dimensional wave maps into surfaces. (joint with Sung-Jin Oh)

Abstract:

The recently established threshold theorem of Sterbenz and Tataru for energy critical wave maps states that wave maps with energy less than that of the ground state (i.e., a minimal energy nontrivial harmonic map) are globally regular and scattering on $\mathbb{R}^{1+2}$. In this talk we give a refinement of this theorem when the target is a closed orientable surface by taking into account an additional  invariant of the problem, namely the topological degree. We show that the sharp energy threshold for global regularity and scattering is in fact \emph{twice} the energy of the ground state for wave maps with degree zero, whereas wave maps with nonzero degree necessarily have at least the energy of the ground state.