#### 54 Citations

The second main theorem of hypersurfaces in the projective space

- Mathematics
- 2012

We deal with a holomorphic map from the complex plane $${\mathbb{C}}$$ to the n-dimensional complex projective space $${\mathbb{P}^{n}(\mathbb{C})}$$ and prove the Nevanlinna Second Main Theorem for… Expand

Analytic and rational sections of relative semi-abelian varieties

- Mathematics
- 2020

The hyperbolicity statements for subvarieties and complements of hypersurfaces in abelian varieties admit arithmetic analogues, due to Faltings (and Vojta for the semi-abelian case). In Atti Accad.… Expand

Recent results on the Kobayashi and Green-Griffiths-Lang conjectures

- Mathematics
- 2018

The study of entire holomorphic curves contained in projective algebraic varieties is intimately related to fascinating questions of geometry and number theory—especially through the concepts of… Expand

Title Some Problems in Value Distribution and Hyperbolic Manifolds : Dedicated to Professor S. Kobayashi(HOLOMORPHIC MAPPINGS, DIOPHANTINE GEOMETRY and RELATED TOPICS : in Honor of Professor

- 2016

Some Problems in Value Distribution and Hyperbolic Manifolds : Dedicated to Professor S. Kobayashi(HOLOMORPHIC MAPPINGS, DIOPHANTINE GEOMETRY and RELATED TOPICS : in Honor of Professor Shoshichi… Expand

Curves in quadric and cubic surfaces whose complements are Kobayashi hyperbolically imbedded

- Mathematics
- 2015

— We construct smooth irreducible curves of the lowest possible degrees in quadric and cubic surfaces whose complements are Kobayashi hyperbolically imbedded into those surfaces. Moreover we… Expand

RECENT PROGRESS TOWARDS THE KOBAYASHI AND GREEN-GRIFFITHS-LANG CONJECTURES

- Mathematics
- 2015

The study of entire holomorphic curves contained in projective algebraic varieties is intimately related to fascinating questions of geometry and number theory – especially through the concepts of… Expand

Entire Curves in Algebraic Varieties

- Mathematics
- 2014

In Chap. 3 the Second Main Theorem for differentiably non-degenerate meromorphic mappings f:C m →V into a projective algebraic manifold V of dimV≦m was established in a satisfactory form. It is the… Expand

Entire Curves in Semi-abelian Varieties

- Mathematics
- 2014

The value distribution of entire curves f from C into semi-abelian varieties A is studied here. We first study the order functions and the structure of the Zariski closures of their jet images J k… Expand

Degeneracy of Holomorphic Curves into Algebraic Varieties II

- Mathematics
- 2013

In our former paper (Noguchi et al. in J. Math. Pures Appl. 88:293–306, 2007) we proved an algebraic degeneracy of entire holomorphic curves into a variety X which carries a finite morphism to a… Expand

Holomorphic Maps with Large Images

- Mathematics
- 2013

We show that each pseudoconvex domain $$\Omega \subset {\mathbb {C}}^n$$Ω⊂Cn admits a holomorphic map $$F$$F to $${\mathbb {C}}^m$$Cm with $$|F|\le C_1 e^{C_2 \hat{\delta }^{-6}}$$|F|≤C1eC2δ^-6,… Expand