Gaussian Decay of the Magnetic Eigenfunctions.
Geometric renormalization of large energy wave maps
There has been much progress in recent years in understanding the existence problem for wave maps with small critical Sobolev norm (in particular for two-dimensional wave maps with small energy); a key aspect in that theory has been a renormalization procedure (either a geometric Coulomb gauge, or a microlocal gauge) which converts the nonlinear term into one closer to that of a semilinear wave equation. However, both of these renormalization procedures encounter difficulty if the energy of the...
Global maximal estimates for solutions to the Schrödinger equation
Global maximal estimates are considered for solutions to an initial value problem for the Schrödinger equation.