Related papers: Schwarz lemma for harmonic mappings between Rieman…
We study harmonic surfaces in $\mathbb{R}^3$ through the framework of harmonic Enneper immersions and prove a superposition principle for such surfaces. We prove that minimal and maximal surfaces admit a decomposition into harmonic…
We calculate the Wess-Zumino term $\Gamma(g)$ for a harmonic map $g$ of a closed surface to a compact, simply connected, simple Lie group $G$ in terms of the energy and the holonomy of the Chern-Simons line bundle on the moduli space of…
The Schwarz--Pick lemma is a fundamental result in complex analysis. It is well-known that Yau generalized it to the higher dimensional manifolds by applying his maximum principle for complete Riemannian manifolds. Jeffres obtained Schwarz…
The aim of this paper is twofold. One is to introduce the class of harmonic $\nu$-Bloch-type mappings as a generalization of harmonic $\nu$-Bloch mappings and thereby we generalize some recent results of harmonic $1$-Bloch-type mappings…
In this paper, we discuss some properties on hyperbolic-harmonic mappings in the unit ball of $\mathbb{C}^{n}$. First, we investigate the relationship between the weighted Lipschitz functions and the hyperbolic-harmonic Bloch spaces. Then…
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…
In order to compare and interpolate signals, we investigate a Riemannian geometry on the space of signals. The metric allows discontinuous signals and measures both horizontal (thus providing many benefits of the Wasserstein metric) and…
This is a survey article to appear in the "Handbook on Teichmueller Theory".
We give an elementary and self-contained proof of the uniformization theorem for non-compact simply-connected Riemann surfaces.
The symmetrized bidisc ${\textbf{G}}_{2}$ is defined by $${\textbf{G}}_{2}:=\{(z_1+z_2,z_1z_2)\in\mathbb{C}^2: |z_1|<1,|z_2|<1,\; z_1,z_2\in\mathbb{C}\}.$$ It is a bounded inhomogeneous pseudoconvex domain without $\mathcal{C}^1$ boundary,…
A general Lefschetz formula for the geodesic action on locally symmetric spaces is proven.
We propose an affine version of the Schwarz map for the hypergeometric differential equation, and study its image when the monodromy group is finite.
We construct harmonic diffeomorphisms from the complex plane $C$ onto any Hadamard surface $M$ whose curvature is bounded above by a negative constant. For that, we prove a Jenkins-Serrin type theorem for minimal graphs in $M\times R$ over…
In this paper, we study the Lehmer's type congruences for lacunary harmonic sums.
Let $(\Sigma,p)$ be a pointed Riemann surface of genus $g\geq 1$. For any integer $k\geq 1$, we parametrize the space of meromorphic quadratic differentials on $\Sigma$ with a pole of order $(k+2)$ at $p$, having a connected critical graph…
In this article, we study Conformal pointwise-slant Riemannian maps (\textit{CPSRM}) from or to K\"{a}hler manifolds to or from Riemannian manifolds. To check the existence of such maps, we provide some non-trivial examples. We derive some…
Riemann surfaces are two-dimensional manifolds with a conformal class of metrics. It is well known that the harmonic action functional and harmonic maps are tools to study the moduli space of Riemann surfaces. Super Riemann surfaces are an…
It is proved some results about existence and non existence of unit normal sections of submanifolds of the Euclidean space and sphere which associated Gauss maps are harmonic. Some applications to CMC hypersurfaces of the sphere and…
A discrete harmonic surface is a trivalent graph which satisfies the balancing condition in the 3-dimensional Euclidean space and achieves energy minimizing under local deformations. Given a topological trivalent graph, a holomorphic…
We introduce slant Riemannian maps from Riemannian manifolds to almost Hermitian manifolds as a generalization of slant immersions, invariant Riemannian maps and anti-invariant Riemannian maps. We give examples, obtain characterizations and…