Geometric Renormalization Below the Ground State

Abstract

The caloric gauge was introduced in [38] by Tao with studying large data energy-critical wave maps mapping from R2+1 to hyperbolic space Hm in view. In [1] Bejenaru et al. adapted the caloric gauge to the setting of Schrödinger maps from Rd+1 to the standard sphere S2↪R3 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, which for maps is the natural limitation imposed by the harmonic map heat flow used to define the caloric gauge. In [34] we apply these results to the study of Schrödinger maps lying below the ground-state energy.

Locations

• International Mathematics Research Notices - View
• arXiv (Cornell University) - View - PDF
• DataCite API - View