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pro vyhledávání: '"32h30"'
Autor:
Dong, Xianjing
Motivated by invalidness of Liouville property for harmonic functions on the connected sum $\#^\vartheta\mathbb C^m$ with $\vartheta\geq2,$ we study Nevanlinna theory on a complete K\"ahler connected sum $$M=M_1\#\cdots\# M_\vartheta$$ with $\varthet
Externí odkaz:
http://arxiv.org/abs/2409.10243
Autor:
Bharti, Nikhil, Van Thin, Nguyen
Let $M$ be a complete complex Hermitian manifold with metric $E_{M}$ and let $\varphi: [0,\infty)\rightarrow (0,\infty)$ be positive function such that $$\gamma_r=\sup\limits_{r\leq a
Externí odkaz:
http://arxiv.org/abs/2408.06800
Autor:
Dong, Xianjing, Liu, Mengyue
Nevanlinna's unicity theorems have always held an important position in value distribution theory. The main purpose of this paper is to generalize the classical Nevanlinna's unicity theorems to non-compact complete Kahler manifolds with nonpositive s
Externí odkaz:
http://arxiv.org/abs/2408.05259
Autor:
Dong, Xianjing
We study Nevanlinna theory of meromorphic mappings from a geodesic ball of a general complete K\"ahler manifold with non-negative Ricci curvature into a complex projective manifold by introducing a heat kernel method. When dimension of a target manif
Externí odkaz:
http://arxiv.org/abs/2406.11623
Autor:
Dong, Xianjing
We study the classical Picard's problem for complete K\"ahler manifolds with non-negative Ricci curvature. Based on the global Green function method, we generalize the Nevanlinna theory to complete K\"ahler manifolds with non-negative Ricci curvature
Externí odkaz:
http://arxiv.org/abs/2405.09659
Autor:
Tsukamoto, Masaki
The main purpose of this paper is to propose an ergodic theoretic approach to the study of entire holomorphic curves. Brody curves are one-Lipschitz holomorphic maps from the complex plane to the complex projective space. They naturally form a dynami
Externí odkaz:
http://arxiv.org/abs/2403.11442
Autor:
Huynh, Dinh Tuan
Publikováno v:
Pacific J. Math. 330 (2024) 157-170
We prove that the Gauss map of a non-flat complete minimal surface immersed in $\mathbb{R}^n$ can omit a generic hypersurface $D$ of degree at most $ n^{n+2}(n+1)^{n+2}$.
Comment: 13 pages, comments are welcome. arXiv admin note: text overlap wi
Comment: 13 pages, comments are welcome. arXiv admin note: text overlap wi
Externí odkaz:
http://arxiv.org/abs/2401.07195
Autor:
Dong, Xianjing
We extend the classical theory of algebroid functions on the complex plane to complex manifolds. The major work is to establish the Nevanlinna theory of algebroid functions on complete K\"ahler manifolds. As its applications, we consider some propaga
Externí odkaz:
http://arxiv.org/abs/2311.07360
Autor:
Haldar, Goutam
The equation $f^n+g^n=1$, $n\in\mathbb{N}$ can be regarded as the Fermat Diophantine equation over the function field. In this paper we study the characterization of entire solutions of some system of Fermat type functional equations by taking $e^{g_
Externí odkaz:
http://arxiv.org/abs/2310.20358
Autor:
Haldar, Goutam
In this paper we establish some results about the existence and precise forms of finite order entire solutions of some systems of quadratic trinomial functional equations one of which in $\mathbb{C}^n$, $n\in\mathbb{N}$ and other two in $\mathbb{C}^2
Externí odkaz:
http://arxiv.org/abs/2311.00011