  We develop the celebrated semigroup approach \`a la Bakry et al on Finsler
manifolds, where natural Laplacian and heat semigroup are nonlinear, based on
the Bochner-Weitzenb\"ock formula established by Sturm and the author. We show
the $L^1$-gradient estimate on Finsler manifolds (under some additional
assumptions in the noncompact case), which is equivalent to a lower weighted
Ricci curvature bound and the improved Bochner inequality. As a geometric
application, we prove Bakry-Ledoux's Gaussian isoperimetric inequality, again
under some additional assumptions in the noncompact case. This extends
Cavalletti-Mondino's inequality on reversible Finsler manifolds to
non-reversible metrics, and improves the author's previous estimate, both based
on the localization (also called needle decomposition) method.
