  We describe a mathematically rigorous differential model for B-type
open-closed topological Landau-Ginzburg theories defined by a pair $(X,W)$,
where $X$ is a non-compact K\"ahlerian manifold with holomorphically trivial
canonical line bundle and $W$ is a complex-valued holomorphic function defined
on $X$ and whose critical locus is compact but need not consist of isolated
points. We also show how this construction specializes to the case when $X$ is
Stein and $W$ has finite critical set, in which case one recovers a simpler
mathematical model.
