The log minimal model program for Kähler 3-folds

In this article we show that the log minimal model program for $\mathbb{Q}$ -factorial dlt pairs ( $X, B$ ) on a compact Kähler 3-fold holds. More specifically, we show that after finitely many divisorial contractions and flips we obtain either a (log) minimal model or a Mori fiber space. We also prove a base point free theorem for Kähler 3-folds.