Stability of the (two-loop) Renormalization Group Flow for Nonlinear Sigma Models

Understand

We prove the stability of the torus, and with suitable rescaling, hyperbolic space under the (two-loop) renormalization group flow for the nonlinear sigma model.

• To prove stability we use similar techniques to \cite{GIK02}, where the stability of the torus under Ricci flow was first established.
• The main technical tool is maximal regularity theory.