We prove the abundance theorem for log canonical $n$-folds such that the boundary divisor is big assuming the abundance conjecture for log canonical $(n-1)$-folds. We also discuss the log minimal model program for log canonical 4-folds.
"Remarks on the abundance conjecture." Proc. Japan Acad. Ser. A Math. Sci. 92 (9) 101 - 106, November 2016. https://doi.org/10.3792/pjaa.92.101