相关论文: Boundary Values and Boundary Uniqueness of $J$-Hol…
We prove a Fatou type theorem for bounded functions with d_J -bar differential of a controled growth on smoothly bounded domains in an almost complex manifold.
The classical Fatou theorem identifies bounded harmonic functions on the unit disk with bounded measurable functions on the boundary circle. We extend this theorem to bounded harmonic maps.
We survey recent progress in a program aimed at proving general Fatou-type results and establishing the well-posedness of a variety of boundary value problems in the upper half-space ${\mathbb{R}}^n_{+}$ for second-order, homogeneous,…
Suppose $G$ is a locally solid lattice group. It is known that there are non-equivalent classes of bounded homomorphisms on $G$ which have topological structures. In this paper, our attempt is to assign lattice structures on them. More…
In this paper, we used some theorems of fixed point for studying the results of Existence and Uniqueness For Hilfer-Hadamard-Type Fractional Differential Equations, \[_{H}D^{\alpha,\beta}x(t)+f(t,x(t))=0, ~~~~~~ on~~the~~ interval~~…
We prove an analogue of Alexander's Theorem for holomorphic mappings of the unit ball in a complex Hilbert space: Every holomorphic mapping which takes a piece of the boundary of the unit ball into the boundary of the unit ball and whose…
We extend a well-known result, about the unit ball, by H. Alexander to a class of balanced domains in $\mathbb{C}^n, \ n > 1$. Specifically: we prove that any proper holomorphic self-map of a certain type of balanced, finite-type domain in…
We study the fixed point sets of holomorphic self-maps of a bounded domain in ${\Bbb C}^n$. Specifically we investigate the least number of fixed points in general position in the domain that forces any automorphism (or endomorphism) to be…
In this paper we study the problems of the following kind: For a pair of topological spaces $X$ and $Y$ find sufficient conditions that under every continuous map $f : X\to Y$ a pair of sufficiently distant points is mapped to a single…
Let $f$ be an analytic function mapping the unit disk $\D$ to itself. We give necessary and sufficient conditions on the local behavior of $f$ near a finite set of boundary points that requires $f$ to be a finite Blaschke product.
In this paper, we establish two new versions of Landau-type theorems for pluriharmonic mappings with a bounded distortion. Then using these results, we derive three Bloch-type theorems of pluriharmonic mappings, which improve the…
We prove a characterization for BLD-mappings between locally complete locally compact path-metric spaces. As a corollary we obtain a sharp limit theorem for BLD-mappings.
By constructing solutions of a singular boundary value problem we prove the existence of a countably infinite family of harmonic self-maps of $\mbox{SU}(3)$ with non-trivial, i.e. $\neq 0,\pm 1$, Brouwer degree.
We prove several Liouville theorems for F-harmonic maps from some complete Riemannian manifolds by assuming some conditions on the Hessian of the distance function, the degrees of F(t) and the asymptotic behavior of the map at infinity. In…
This paper presents and explores a theory of \emph{multiholomorphic maps}. This group of ideas generalizes the theory of pseudoholomorphic curves in a direction suggested by consideration of the kinds of compatible geometric structures that…
We obtain a Blaschke-type necessary conditions on zeros of analytic functions on the unit disk with different types of exponential growth at the boundary. These conditions are used to prove Lieb-Thirring-type inequalities for the…
In this paper, we first define two classes of holomorphic mappings defined on the unit ball $B^n$ of n-dimensional complex space $\mathbb{C}^n$ and obtain the lower estimates for Bloch's constant for these classes. Also, we derive the…
The fundamental properties of $J$-holomorphic maps depend on two inequalities: The gradient inequality gives a pointwise bound on the differential of a $J$-holomorphic map in terms of its energy. The cylinder inequality stipulates and…
We prove an existence theorem for the sliding boundary variant of the Plateau problem for $2$-dimensional sets in $\mathbb{R}^n$. The simplest case of sufficient condition is when $n=3$ and the boundary $\Gamma$ is a finite disjoint union…
We show that $J-$ stability is open and dense in natural families of meromorphic maps of one complex variable with a finite number of singular values, and even more generally, to finite type maps. This extends the results of…