相关论文: Cellular harmonic maps which are not diffeomorphis…
We prove that a harmonic quasi-isometric map between pinched Hadamard surfaces is a quasi-conformal diffeomorphism.
We present simple examples of finite-dimensional connected homogeneous spaces (they are actually topological manifolds) with nonhomogeneous and nonrigid factors. In particular, we give an elementary solution of an old problem in general…
We classify closed, simply-connected, non-negatively curved 6-manifolds of almost maximal symmetry rank up to equivariant diffeomorphism.
Non-polynomial growth harmonic maps from the complex plane to the hyperbolic space are studied. Some non-surjectivity results are obtained. Moreover, images of such harmonic maps are investigated with reference to their Hopf differentials.
In this note we show that a compact asymptotically harmonic manifold without focal points is either flat or a rank one locally symmetric space.
In this paper biharmonic maps between doubly warped product manifolds are studied. We show that the inclusion maps of Riemannian manifolds $B$ and $F$ into the doubly warped product $_{f}B\times_{b}F$ can not be proper biharmonic maps. Also…
A Lie group $G$ endowed with a left invariant Riemannian metric $g$ is called Riemannian Lie group. Harmonic and biharmonic maps between Riemannian manifolds is an important area of investigation. In this paper, we study different aspects…
In this paper we generalize harmonic maps and morphisms to the \emph{degenerate semi-Riemannian category}, in the case when the manifolds $M$ and $N$ are \emph{stationary} and the map $\phi :M\to N$ is \emph{radical-preserving}. We…
A unicellular map is the embedding of a connected graph in a surface in such a way that the complement of the graph is a topological disk. In this paper we present a bijective link between unicellular maps on a non-orientable surface and…
It is shown that smooth maps $f: S^3 \rightarrow S^3$ contain two countable families of harmonic representatives in the homotopy classes of degree zero and one.
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…
A Riemannian manifold is called harmonic if its volume density function expressed in polar coordinates centered at any point is radial. Flat and rank-one symmetric spaces are harmonic. The converse (the Lichnerowicz Conjecture) is true for…
Let $f$ be a harmonic map from a Riemann surface to a Riemannian $n$-manifold. We prove that if there is a holomorphic diffeomorphism $h$ between open subsets of the surface such that $f\circ h = f$, then $f$ factors through a holomorphic…
We study the degrees of homogeneous harmonic maps between simplicial cones. Such maps have been used to model the local behavior of harmonic maps between singular spaces, where the degrees of homogeneous approximations describe the…
f-Biharmonic maps are the extrema of the f-bienergy functional. f-biharmonic submanifolds are submanifolds whose defining isometric immersions are f-biharmonic maps. In this paper, we prove that an f-biharmonic map from a compact Riemannian…
In this paper, we will prove a result of nonexistence on harmonic diffeomorphisms between punctured spaces. In particular, we will given an elementary proof to the nonexistence of rotationally symmetric harmonic diffeomorphisms from the…
We classify all tight holomorphic maps between Hermitian symmetric spaces of non-compact type.
In this paper, we study the existence of harmonic and bi-harmonic maps into Riemannian manifolds admitting a conformal vector field, or a nontrivial Ricci solitons.
We show that the notions of homotopy epimorphism and homological epimorphism in the category of differential graded algebras are equivalent. As an application we obtain a characterization of acyclic maps of topological spaces in terms of…
In this paper, we introduce metallic maps between metallic Riemannian manifolds, provide an example and obtain certain conditions for such maps to be totally geodesic. We also give a sufficient condition for a map between metallic…