2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/202040We 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.May differ slightly from the published versionHigh Energy Physics - Theorytext