Related papers: Harmonic maps from $\mathbb{C}^{n}$ to Kahler mani…

In this paper we study the set of balanced metrics (in Donaldson's terminology) on a compact complex manifold M which are homothetic to a given balanced one. This question is related to various properties of the Tian-Yau-Zelditch…

We introduce the complete lifts of maps between (real and complex) Euclidean spaces and study their properties concerning holomorphicity, harmonicity and horizontal weakly conformality. As applications, we are able to use this concept to…

Continuous mappings between compact Hausdorff spaces can be studied using homomorphisms between algebraic structures (lattices, Boolean algebras) associated with the spaces. This gives us more tools with which to tackle problems about these…

We obtain a topological interpretation for the space of $L^2$ harmonic forms for some complete Riemannian manifold : when the geometry at infinity is the geometry of a simply connected nilpotent Lie group, when the geometry at infinity is a…

We study representations of lattices of PU(m,1) into PU(n,1). We show that if a representation is reductive and if m is at least 2, then there exists a finite energy harmonic equivariant map from complex hyperbolic m-space to complex…

Harmonic maps are nonlinear extensions of harmonic functions. They are critical points of natural energy functionals between Riemannian manifolds. Such type of problems appear in Physics, Geometry of Finance and the study of regularity and…

In this paper, we discuss the heat flow of a pseudo-harmonic map from a closed pseudo-Hermitian manifold to a Riemannian manifold with non-positive sectional curvature, and prove the existence of the pseudo-harmonic map which is a…

In this work we construct a variety of new complex-valued proper biharmonic maps and (2,1)-harmonic morphisms on Riemannian manifolds with non-trivial geometry. These are solutions to a non-linear system of partial differential equations…

Our main result in this paper is the following: Given $H^m, H^n$ hyperbolic spaces of dimensional $m$ and $n$ corresponding, and given a Holder function $f=(s^1,...,f^{n-1}):\partial H^m\to \partial H^n$ between geometric boundaries of…

Suppose $G$ is a connected complex Lie group and $H$ is a closed complex subgroup such that $X := G/H$ is Kaehler and the codimension of the top non-vanishing homology group of $X$ with coefficients in $\mathbb Z_2$ is less than or equal to…

Let $\Sigma$ be a compact Riemann surface and $D_1,...,D_n$ a finite number of pairwise disjoint closed disks of $\Sigma$. We prove the existence of a proper harmonic map into the Euclidean plane from a hyperbolic domain $\Omega$ containing…

We give a topological interpretation of the space of $L^2$-harmonic forms on Manifold with flat ends. It is an answer to an old question of J. Dodziuk. We also give a Chern-Gauss-Bonnet formula for the $L^2$-Euler characteristic of some of…

We show that if $E$ is a closed convex set in $\mathbb C^n$ $(n>1)$ contained in a closed halfspace $H$ such that $E\cap bH$ is nonempty and bounded, then the concave domain $\Omega = \mathbb C^n\setminus E$ contains images of proper…

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…

Using a flow first introduced by J.P. Anderson, we obtain some existence theorems for harmonic maps from a noncompact complete Riemannian manifold into a complete Riemannian manifold. In particular, we prove as a corollary a recent result…

In this paper, we investigate critical maps of the horizontal energy functional $E_{H,\widetilde{H}}(f)$ for maps between two pseudo-Hermitian manifolds $(M^{2m+1},H(M),J,\theta )$ and $(N^{2n+1},\widetilde{H}(N),…

Let (M,g) be a simply connected complete Kahler manifold with nonpositive sectional curvature. Assume that g has constant negative holomorphic sectional curvature outside a compact set. We prove that M is then biholomorphic to the unit ball…

We give the following positive answer to Gromov's question (in "Oka's principle for holomorphic sections of elliptic bundles", J. Amer. Math. Soc. 2, 851-897 (1989), 3.4.(D), page 881). THEOREM: If every holomorphic map from a compact…

We compute a Simons' type formula for the stress-energy tensor of biharmonic maps from surfaces. Specializing to Riemannian immersions, we prove several rigidity results for biharmonic CMC surfaces, putting in evidence the influence of the…

A manifold M is locally conformally Kahler (LCK) if it admits a Kahler covering with monodromy acting by holomorphic homotheties. For a compact connected group G acting on an LCK manifold by holomorphic automorphisms, an averaging procedure…