Geometric renormalization below the ground state

Abstract

The caloric gauge was introduced by Tao with studying large data energy critical wave maps mapping from $\mathbf{R}^{2+1}$ to hyperbolic space $\mathbf{H}^m$ in view. In \cite{BIKT} Bejenaru, Ionescu, Kenig, and Tataru adapted the caloric gauge to the setting of Schrödinger maps from $\mathbf{R}^{d + 1}$ to the standard sphere $S^2 \hookrightarrow \mathbf{R}^3$ with initial data small in the critical Sobolev norm. Here we develop the caloric gauge in a bounded geometry setting with a construction valid up to the ground state energy.

39 pages; Typos and argument for noncompact target manifolds corrected; Published form available at http://imrn.oxfordjournals.org/cgi/content/abstract/rnr169?ijkey=OXVb8Exb1XuXqLz&keytype=ref