Vanishing theorems for $(k, s)$-positive vector bundles on weakly pseudoconvex Kähler manifolds

We will use analytic methods in this paper, based on $L^2$-methods for the $\overline{\partial}$-equation, to obtain some new vanishing theorems for holomorphic vector bundles of $(k, s)$-positivity on weakly pseudoconvex Kähler manifolds which generalize those obtained by Demailly for $s$-positive vector bundles in his sense.

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Received 4 November 2017

Published 21 December 2018