Tohoku Mathematical Journal
2021

June
SECOND SERIES VOL. 73, NO. 2

Tohoku Math. J.
73 (2021), 199-219

Title NON-INTEGRATED DEFECT RELATION FOR MEROMORPHIC MAPS FROM KÄHLER MANIFOLDS WITH HYPERSURFACES OF A PROJECTIVE VARIETY IN SUBGENERAL POSITION

Author Si Duc Quang, Le Ngoc Quynh and Nguyen Thi Nhung

(Received March 22, 2018, revised June 19, 2019)
Abstract. In this article, we establish a truncated non-integrated defect relation for meromorphic mappings from a complete Kähler manifold into a projective variety intersecting a family of hypersurfaces located in subgeneral position, where the truncation level of the defect is explicitly estimated. Our result generalizes and improves previous results. In particular, when the family of hypersurfaces located in general position, our result will implies the previous result of Min Ru-Sogome. In the last part of this paper we will apply our result to study the distribution of the Gauss maps of minimal surfaces.

Mathematics Subject Classification. Primary 32H30; Secondary 32A22, 30D35.

Key words and phrases. Nevanlinna, second main theorem, meromorphic mapping, non-integrated defect relation.

To the top of this page

Back to the Contents