Min Ru

Nevanlinna Theory and Its Relation to Diophantine Approximation

Nevanlinna Theory for Meromorphic Functions and Roths Theorem Holomorphic Curves into Compact Riemann Surfaces and Theorems of Siegel, Roth, and Faltings Holomorphic Curves in Pn(C) and Schmidts Sub-Space Theorem The Moving Target Problems Equi-Dimensional Nevanlinna Theory and Vojtas Conjecture Holomorphic Curves in Abelian Varieties and the Theorem of Faltings Complex Hyperbolic Manifolds and Langs Conjecture.

The second main theorem for moving targets

AbstractThe defect relation for holomorphic maps

Gauss map of minimal surfaces with ramification

f:\mathbb{C} \to \mathbb{P}_n

Algebroid functions, Wirsing's theorem and their relations

in respect to slowly moving target hyperplanes in

Non-integrated defect relation for meromorphic maps of complete Kähler manifolds into ℙⁿ(ℂ) intersecting hypersurfaces

\mathbb{P}_n

Uniqueness of holomorphic curves into abelian varieties

is proved. The sharp defect boundn+1 is obtained.