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Subjects
32-XX Several complex variables and analytic spaces
32Lxx Holomorphic fiber spaces
32L20 Vanishing theorems

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Holomorphic Morse Inequalities on Manifolds with Boundary

Robert Berman (2005)

Annales de l’institut Fourier

Let $X$ be a compact complex manifold with boundary and let $L^{k}$ be a high power of a hermitian holomorphic line bundle over $X .$ When $X$ has no boundary, Demailly’s holomorphic Morse inequalities give asymptotic bounds on the dimensions of the Dolbeault cohomology groups with values in $L^{k},$ in terms of the curvature of $L .$ We extend Demailly’s inequalities to the case when $X$ has a boundary by adding a boundary term expressed as a certain average of the curvature of the line bundle and the Levi curvature of the...

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