Demailly, Jean Pierre Holomorphic Morse inequalities. (English) Zbl 0755.32008 Several complex variables and complex geometry, Proc. Summer Res. Inst., Santa Cruz/CA (USA) 1989, Proc. Symp. Pure Math. 52, Part 2, 93-114 (1991). [For the entire collection see Zbl 0732.00008.]In this paper the complex analogues of the Morse inequalities for \(\overline\partial\)-cohomology groups with values in holomorphic vector bundles are explained, and some applications of that theory are presented. Reviewer: B.Nowak (Łódź) Cited in 1 ReviewCited in 22 Documents MSC: 32C35 Analytic sheaves and cohomology groups 58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces 32L10 Sheaves and cohomology of sections of holomorphic vector bundles, general results 53C07 Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) Keywords:\(\overline\partial\)-cohomology groups; Morse inequalities; holomorphic vector bundles Citations:Zbl 0732.00008 PDFBibTeX XMLCite \textit{J. P. Demailly}, Proc. Symp. Pure Math. None, 93--114 (1991; Zbl 0755.32008)