Bott-Chern harmonic forms on Stein manifolds

Abstract:

Let $M$ be an $n$-dimensional $d$-bounded Stein manifold $M$, i.e., a complex $n$-dimensional manifold $M$ admitting a smooth strictly plurisubharmonic exhaustion $\rho$ and endowed with the Kähler metric whose fundamental form is $\omega =i\partial \overline {\partial }\rho$, such that $i\overline {\partial }\rho$ has bounded $L^\infty$ norm. We prove a vanishing result for $W^{1,2}$ harmonic forms with respect to the Bott-Chern Laplacian on $M$.