Log version of Campana--Peternell's conjecture

Let $X$ be a projective log canonical variety, and suppose that $-K_X$ is a strictly nef divisor. Log version of Campana--Peternell's conjecture. The anti-canonical divisor $-K_X$ is ample. This is the singular, zero-boundary case of the log version of Serrano's conjecture. The paper proves this in dimension three for log canonical varieties and obtains partial results in dimension four; the general statement remains open.