Tohoku Mathematical Journal
2026
June
SECOND SERIES VOL. 78, NO. 2

Tohoku Math. J.
78 (2026), 173-195

Title LOGARITHMIC AKIZUKI--NAKANO VANISHING THEOREMS ON WEAKLY PSEUDOCONVEX KÄHLER MANIFOLDS

Author Yongpan Zou

(Received January 15, 2024, revised June 10, 2024)
Abstract. In this paper, we establish a logarithmic vanishing theorem on weakly pseudoconvex Kähler manifolds, where the divisor may have infinitely many irreducible components. This result serves as a generalization of Norimatsu's findings on compact Khler manifolds. We derive vanishing theorems for certain direct image sheaves as a direct corollary.

Mathematics Subject Classification. Primary 32E05; Secondary 32E30, 32T35.
Key words and phrases. Logarithmic vanishing theorem, weakly pseudoconvex Kähler manifold, Runge approximation.

To the top of this page

Back to the Contents