Oberseminar: Bingxiao Liu (G.15.25)
In this talk, I will present a general Nakano–Griffiths type inequality with boundary terms. We then apply this result to derive holomorphic Morse inequalities for bounded domains satisfying appropriate concavity assumptions, through an analysis of the spectral spaces of the Kodaira–Hodge Laplacian under $\overline{\partial}$-Neumann boundary condition. As applications, we obtain a criterion for Moishezon $1$-concave manifolds and, in combination with a theorem of Kohn–Rossi, an extension theorem for Levi $q$-concave domains. This talk is based on joint work with George Marinescu (University of Cologne) and Huan Wang (Henan Academy of Sciences).
