2019
Том 71
№ 8

All Issues

Si Duc Quang

Articles: 4
Article (English)

Unicity theorems with truncated multiplicities of meromorphic mappings in several complex variables for few fixed targets

Pham Hoang Ha, Si Duc Quang

↓ Abstract

Ukr. Mat. Zh. - 2019. - 71, № 3. - pp. 412-432

The purpose of our paper is twofold. Our first aim is to prove a uniqueness theorem for meromorphic mappings of $C^n$ into $P^N(C)$ sharing $2N + 2$ hyperplanes in the general position with truncated multiplicities, where all common zeros with multiplicities more than a certain number do not need to be counted. Second, we consider the case of mappings sharing less than $2N + 2$ hyperplanes. These results are improvements of some recent results.

Article (English)

Big Picard Theorem for Meromorphic Mappings with Moving Hyperplanes in $P_n (C)$

Si Duc Quang

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2014. - 66, № 11. - pp. 1550–1562

We present some extension theorems in the style of the Big Picard theorem for meromorphic mappings of $C_m$ into $P_n (C)$ with a few moving hyperplanes.

Article (English)

Extension of holomorphic mappings for few moving hypersurfaces

Si Duc Quang

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2012. - 64, № 3. - pp. 392-403

We prove the big Picard theorem for holomorphic curves from a punctured disc into $P^n(C)$ with $n + 2$ hypersurfaces. We also prove a theorem on the extension of holomorphic mappings in several complex variables into a submanifold of$P^n(C)$ with several moving hypersurfaces.

Brief Communications (English)

On the Relation between Curvature, Diameter, and Volume of a Complete Riemannian Manifold

Nguyen Doan Tuan, Si Duc Quang

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2004. - 56, № 11. - pp. 1576–1583

In this note, we prove that if N is a compact totally geodesic submanifold of a complete Riemannian manifold M, g whose sectional curvature K satisfies the relation Kk > 0, then \(d(m,N) \leqslant \frac{\pi }{{2\sqrt k }}\) for any point mM. In the case where dim M = 2, the Gaussian curvature K satisfies the relation Kk ≥ 0, and γ is of length l, we get Vol (M, g) ≤ \(\frac{{2l}}{{\sqrt k }}\) if k ≠ 0 and Vol (M, g ≤ 2ldiam (M) if k = 0.