Anomaly Flow: Shi-Type Estimates and Long-time Existence

Abstract

We consider the long-time existence of the anomaly flow on a compact complex $3$-fold with general slope parameter $\hat{I}{\pm }^{\prime }$. In particular, we obtain integral Shi-type estimates for the flow by adapting a integration-by-parts type argument instead of the usual maximum principle techniques. Following this, we prescribe a sufficient smallness condition on $\hat{I}{\pm }^{\prime }$ in order to extend the flow on $[0,\ddot{I}„)$ to $[0,\ddot{I}„+\hat{I}\mu )$.

35 Pages. Changed Remark 3.1