Logarithmic vanishing theorems on Weakly 1-complete Kahler manifolds

Abstract In this paper, we prove a logarithmic vanishing theorem on weakly 1-complete k\"ahler manifold, which is a generalization of Huang-Liu-Wan-Yang's result on compact k\"ahler manifold. We first briefly introduce the local case of the theorem, which can be obtained as a corollary of the compact k\"ahler case. Next, we prove the global case of the theorem. The difficulty here is how to find a continuous solution from a sequence ᵥ of discrete solutions of equation ᵥ=ᵥ, such that for each v R, ᵥ=. In this paper, the continuous solution is given by using the approximation theorem. 2020 Mathematics Subject Classification. 32Q15, 14F17.