Related papers: Cartan's Conjecture for Moving Hypersurfaces

In this paper, we prove a second main theorem for a holomorphic curve $f$ into $\mathbb P^N (\mathbb C)$ with a family of slowly moving hypersurfaces $D_1,...,D_q$ with respect to $f$ in $m$-subgeneral position, proving an inequality with…

In this paper, we establish a uniqueness theorem for algebraically nondegenerate meromorphic maps of C^m into C P^n and slowly moving hypersurfaces Q_j in C P^n, j=1,...,q in (weakly) general position, where q depends effectively on n and…

Let $f$ be an algebraically nondegenerate meromorphic mapping from $\mathbb C^m$ into $\mathbb P^n(\mathbb C)$ and let $Q_1,...,Q_q$ be $q$ hypersurfaces in $\mathbb P^n(\mathbb C)$ of degree $d_i$, in $N-$subgeneral position. In this…

Let $V$ be a projective subvariety of $\mathbb P^n(\mathbb C)$. A family of hypersurfaces $\{Q_i\}_{i=1}^q$ in $\mathbb P^n(\mathbb C)$ is said to be in $N$-subgeneral position with respect to $V$ if for any $1\le i_1<\cdots <i_{N+1}$, $…

In 1979, B. Shiffman conjectured that if f is an algebraically nondegenerate holomorphic map of C into P^n and D_1,...,D_q are hypersurfaces in P^n in general position, then the sum of the defects is at most n+1. This conjecture was proved…

By using Brownian motion and stochastic calculus, we establish a second main theorem for holomorphic curves into a projective subvariety $V\subset\mathbb P^n(\mathbb C)$ with an arbitrary family $\mathcal Q$ of $q$ hypersurfaces…

In this paper, we establish a general second main theorem for meromorphic mappings from $\mathbb C^m$ into a subvariety $V$ of $\mathbb P^n(\mathbb C)$ with respect to an arbitrary family of slowly moving hypersurfaces $\mathcal…

In this paper, we prove a general second main theorem for meromorphic mappings into a subvariety $V$ of $\mathbb P^N(\mathbb C)$ with an arbitrary family of moving hypersurfaces. Our second main theorem generalizes and improves all previous…

For $q\leq 3$ smooth plane algebraic curves $\mathcal{C}_i$ having simple normal crossings, if the invariant logarithmic $2$-jet differential bundle associated to $(\mathbb{P}^2(\mathbb{C}), \sum_{i=1}^q \mathcal{C}_i)$ has a nonzero…

We establish second main theorems for holomorphic curves into a projective subvary $V \subset \mathbb{P}^n(\mathbb{C})$ of dimension $k$, intersecting hypersurfaces in $N$-subgeneral position with respect to $V$ $(N > k)$. Our results…

In this article, we establish some new second main theorems for meromorphic mappings of $\mathbb C^m$ into $\mathbb P^n(\mathbb C)$ and moving hypersurfaces with truncated counting functions. A uniqueness theorem for these mappings sharing…

In this note, we establish the following Second Main Theorem type estimate for every entire non-algebraically degenerate holomorphic curve $f\colon\mathbb{C}\rightarrow\mathbb{P}^n(\mathbb{C})$, in present of a {\sl generic} hypersuface…

In this paper, we prove a Second Main Theorem for holomorphic mappings in a disk whose image intersects some families of nonlinear hypersurfaces (totally geodesic hypersurfaces with respect to a meromorphic connection) in the complex…

In 1983, Nochka proved a conjecture of Cartan on defects of holomorphic curves in CP^n relative to a possibly degenerate set of hyperplanes. In this paper, we generalize the Nochka's theorem to the case of curves in a complex projective…

If f: C -> P^n is a holomorphic curve of hyper-order less than one for which 2n + 1 hyperplanes in general position have forward invariant preimages with respect to the translation t(z)=z+c, then f is periodic with period c. This result,…

Let $\{D_i\}_{i=1}^{n+1}$ be $n+1$ hypersurfaces in $\mathbb{P}^n(\mathbb{C})$ with total degrees $\sum_{i=1}^{n+1} \deg D_i\geqslant n+2$, in general position and satisfying a generic geometric condition: every $n$ hypersurfaces intersect…

In this paper, by introducing the notion of "\textit{distributive constant}" of a family of hypersurfaces with respect to a projective variety, we prove a second main theorem in Nevanlinna theory for meromorphic mappings with arbitrary…

We prove that if $M$ and $M'$ are algebraic hypersurfaces in $ C^ N$, i.e. both defined by the vanishing of real polynomials, then any sufficiently smooth CR mapping with Jacobian not identically zero extends holomorphically provided the…

The purpose of this paper has twofold. The first is to establish a second main theorem with truncated counting functions for algebraically nondegenerate meromorphic mappings into an arbitrary projective variety intersecting a family of…

The main aim of this article is to give some sufficient conditions for a family of meromorphic mappings on a domain D in C^n into P^N(C) to be meromorphically normal if they satisfy only some very weak conditions with respect to moving…