# The Second main theorem of holomorphic maps on spherically symmetric K\"ahler manifolds

@inproceedings{Dong2021TheSM, title={The Second main theorem of holomorphic maps on spherically symmetric K\"ahler manifolds}, author={Xianjing Dong and Peichu Hu}, year={2021} }

Spherically symmetric manifolds are one class of important Riemannian models in mathematics and physics which includes the most common spaces such as Euclidean spaces, balls and spheres, etc.. In this paper, we consider the Nevanlinna theory concerning value distribution of holomorphic maps from a spherically symmetric Kähler manifold into a complex projective manifold under the assumption that the dimension of sources is not less than one of targets. In our settings, a Second Main Theorem is…

## References

SHOWING 1-10 OF 31 REFERENCES

The second main theorem of holomorphic curves into projective spaces

- Mathematics
- 2011

By utilizing Jacobian sections introduced by Stoll, we prove a second main theorem of holomorphic curves into projective spaces for hypersurfaces under certain conditions on the jets of the curves.…

Nevanlinna Theory and Its Relation to Diophantine Approximation

- Mathematics
- 2001

Nevanlinna Theory for Meromorphic Functions and Roth's Theorem Holomorphic Curves into Compact Riemann Surfaces and Theorems of Siegel, Roth, and Faltings Holomorphic Curves in Pn(C) and Schmidt's…

A Defect Relation for Equidimensional Holomorphic Mappings Between Algebraic Varieties

- Mathematics
- 1972

0. Introduction 1. Notations, terminology, and sign conventions (a) Line bundles and Chern classes (b) Currents and forms in C0 2. Construction of a volume form 3. A second main theorem for…

Nevanlinna-type theorems for meromorphic functions on non-positively curved Kähler manifolds

- Mathematics
- 2017

Abstract We give a second main theorem of Nevanlinna theory on complete non-positively curved Kähler manifolds. Its remainder term depends only on Ricci curvature of the manifolds except for the…

Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds

- Mathematics
- 1999

We provide an overview of such properties of the Brownian motion on complete non-compact Riemannian manifolds as recurrence and non-explosion. It is shown that both properties have various analytic…

Nevanlinna Theory in Several Complex Variables and Diophantine Approximation

- Mathematics
- 2013

Nevanlinna Theory of Meromorphic Functions.- First Main Theorem.- Differentiably Non-Degenerate Meromorphic Maps.- Entire Curves into Algebraic Varieties.- Semi-Abelian Varieties.- Entire Curves into…

Two Applications of Algebraic Geometry to Entire Holomorphic Mappings

- Mathematics
- 1980

In this paper we shall prove two theorems concerning holomorphic mappings of large open sets of ℂk into algebraic varieties. Both are in response to well-known outstanding problems, and we feel that…

Holomorphic curves into algebraic varieties

- Mathematics
- 2009

This paper establishes a defect relation for algebraically nondegenerate holomorphic mappings into an arbitrary nonsingular complex projective variety V (rather than just the projective space)…

Distribution Theory of Algebraic Numbers

- Mathematics
- 2008

The book timely surveys new research results and related developments in Diophantine approximation, a division of number theory which deals with the approximation of real numbers by rational numbers.…

Curvature, geodesics and the Brownian motion on a Riemannian manifold. I. Recurrence properties

- Mathematics
- 1982

Let M be an n -dimensional, complete, connected and locally compact Riemannian manifold and g be its metric. Denote by Δ M the Laplacian on M .