Non-integrated defect relation for meromorphic maps from a Kähler manifold intersecting hypersurfaces in subgeneral of ${\mathbb{P}}^n(\mathbb{C})$

Abstract

In this article, we establish a truncated non-integrated defect relation for meromorphic mappings from an $m$-dimensional complete Kähler manifold into ${\mathbb{P}}^n(\mathbb{C})$ intersecting $q$ hypersurfaces $Q_1,...,Q_q$ in $k$-subgeneral position of degree $d_i$, i.e., the intersection of any $k+1$ hypersurfaces is emptyset. We will prove that $$\sum _{i=1}^q{\delta }_f^{[u-1]}(Q_i)\le (k-n+1)(n+1)+\epsilon +\frac{\rho u(u-1)}{d},$$ where $u$ is explicitly estimated and $d$ is the least common multiple of $d_i^{\prime }$s. Our result generalizes and improves previous results. In the last part of this paper we will apply this result to study the distribution of the Gauss map of minimal surfaces.

19 pages

References in corpus (2)

• Degeneracy second main theorems for meromorphic mappings into projective varieties with hypersurfaces
• Second main theorem for meromorphic mappings with moving hypersurfaces in subgeneral position

Cited by in corpus (5)

• Generalizations of degeneracy second main theorem and Schmidt's subspace theorem
• Non-integrated defect relation for meromorphic mappings from a Kähler manifold with hypersurfaces of a projective variety in subgeneral position
• Improvement of non-integrated defect relation for meromorphic maps from Kähler manifolds
• Algebraic dependence and finiteness problems of differentiably nondegenerate meromorphic mappings on Kähler manifolds
• Meromorphic maps of Kahler manifolds with trivial canonical bundles