arXiv research

Study of holomorphic correspondences combining entire maps and Fuchsian groups.

We propose a new approach to the value distribution theory of entire holomorphic curves. We define a ``packing density'' of an entire holomorphic curve, and show that it has various non-trivial properties. We prove a ``gap theorem'' for holomorphic maps from elliptic curves to the complex projective space, and study th…

Study of hyperbolic behavior in complex manifolds with specific vector bundles.

The paper explores anti-hyperbolicity for hyperkähler varieties.

Characterizes a general range decreasing group homomorphism.

Let $K$ be a closed polydisc or ball in $\C^n$, and let $Y$ be a quasi projective algebraic manifold which is Zariski locally equivalent to $\C^p$, or a complement of an algebraic subvariety of codimension $\ge 2$ in such manifold. If $r$ is an integer satisfying $(n-r+1) (p-r+1)\geq 2$ then every holomorphic map from …

Curves in higher dimensions are either affine or have super-Euclidean energy growth.

Classifies area-minimizing surfaces in R^4 as algebraic.

Introduces quasi-holomorphic maps and their properties.

Harmonic map flow preserves almost-holomorphic maps without singularities.

We introduce holomorphic Riemannian maps between almost Hermitian manifolds as a generalization of holomorphic submanifolds and holomorphic submersions, give examples and obtain a geometric characterization of harmonic holomorphic Riemannian maps from almost Hermitian manifolds to Kaehler manifolds.

Holomorphic maps are a special case of Hermitian pluriharmonic maps between almost Hermitian manifolds.

We classify the entire minimal vertical graphs in the 3 dimensional Heisenberg group Nil endowed with a Riemannian left-invariant metric. This classification, which provides a solution to the Bernstein problem in Nil, is given in terms of the Abresch-Rosenberg holomorphic differential for minimal surfaces in Nil.

Researchers create a projective space for quasimaps and study its connections to Calabi-Yau fibrations.

Holomorphic maps between moduli spaces are shown to be forgetful for large g.

In this paper, we study deformations of holomorphic Poisson maps which extend Horikawa's series of papers on deformations of holomorphic maps in the context of holomorphic Poisson deformations. In appendices, we present deformations of Poisson morphisms in the language of functors of Artin rings which is the algebraic …

The paper proves Liouville theorems for holomorphic maps on pseudo-Hermitian manifolds.

Entire area-minimizing surfaces of density 2 are planar or quadratic

H-holomorphic maps are a parameter version of J-holomorphic maps into contact manifolds. They have arisen in efforts to prove the existence of higher--genus holomorphic open book decompositions and efforts to prove the existence of finite energy foliations and the Weinstein conjecture, as well as in folded holomorphic …

We study proper holomorphic maps between bounded symmetric domains $D$ and $Ω$. In particular, when $D$ and $Ω$ are of the same rank $\ge 2$ such that all irreducible factors of $D$ are of rank $\ge 2$, we prove that any proper holomorphic map from $D$ to $Ω$ is a totally geodesic holomorphic isometric embedding with r…

Let $M$ and $N$ be two compact complex manifolds. We show that if the tautological line bundle $\mathscr{O}_{T_M^*}(1)$ is not pseudo-effective and $\mathscr{O}_{T_N^*}(1)$ is nef, then there is no non-constant holomorphic map from $M$ to $N$. In particular, we prove that any holomorphic map from a compact complex mani…

Local holomorphic maps preserving (p,p) forms are shown to be isometries.

Proves rigidity of maps between balls with Hölder boundary continuity.

The paper proves a factorization theorem for harmonic maps between Riemann surfaces and manifolds.

The paper classifies holomorphic maps between Riemann surface configuration spaces.

The paper resolves a problem about metric inequivalence and characterizes proper holomorphic maps.

Isothermic nets created from special maps for smooth surfaces.

Study proper holomorphic maps between specific domains, proving rigidity under certain conditions.

We classify all tight holomorphic maps between Hermitian symmetric spaces of non-compact type.

As in [5], we study holomorphic maps of positive degree between compact complex manifolds, and prove that any holomorphic map of degree one from a compact complex manifold to itself is biholomorphic. This conclusion confirms that under a mild restriction the holomorphic Gromov relation ">_" is indeed a partial order.

The paper proves a Schwarz lemma for mappings between specific types of manifolds.

Estimates curvature for holomorphic maps on Riemann surfaces.

Paper proves unique tangent maps for complex maps into algebraic varieties.

The paper establishes Schwarz type lemmas for holomorphic maps between pseudo-Hermitian and Hermitian manifolds.

The paper discusses properties of holomorphic one-forms on certain complex manifolds.

Study generalizes map properties between Hermitian manifolds preserving specific forms.

Study global geometry of dynamical systems with entire vector fields.

Study on harmonicity of maps between different types of almost contact metric manifolds.

In this article, we prove a Liouville property of holomorphic maps from a complete Kahler manifold with nonnegative holomorphic bisectional curvature to a complete simply connected Kahler manifold with a certain assumption on the sectional curvature.

In this paper, we consider some generalized holomorphic maps between pseudo-Hermitian manifolds. These maps include the \emph{CR} maps and the transversally holomorphic maps. In terms of some sub-Laplacian or Hessian type Bochner formulas, and comparison theorems in the pseudo-Hermitian version, we are able to establis…

The paper extends Schwarz's lemma to RC-positivity and complex manifolds.

Every oriented 4-manifold admits a folded symplectic structure, which in turn determines a homotopy class of compatible almost complex structures that are discontinuous across the folding hypersurface ("fold") in a controlled fashion. We define folded holomorphic maps, i.e. pseudo-holomorphic maps that are discontinuou…

We define holomorphic quadratic differentials for spacelike surfaces with constant mean curvature in the Lorentzian homogeneous spaces $\mathbb{L}(κ,τ)$ with isometry group of dimension 4, which are dual to the Abresch-Rosenberg differentials in the Riemannian counterparts $\mathbb{E}(κ,τ)$, and obtain some consequence…

Extends holomorphic functions on complex manifolds to larger spaces.

Stable solutions found for a specific physics model.

Constructs the moduli space of super J-holomorphic curves.

Proves singularities of codimension one objects under finite holomorphic maps.

In this article, we study local holomorphic isometric embeddings from ${\BB}^n$ into ${\BB}^{N_1}\times... \times{\BB}^{N_m}$ with respect to the normalized Bergman metrics up to conformal factors. Assume that each conformal factor is smooth Nash algebraic. Then each component of the map is a multi-valued holomorphic m…