Related papers: Harmonic Maps and Teichmueller Theory

This is a survey paper on Alegbraic Geometry over Lie Algebras

We give a sufficient criterion, which we call stability, for a coarse Lipschitz map $f$ from a complete manifold $X$ with Ricci curvature bounded below to a proper Hadamard space $Y$ to be within bounded distance of a harmonic map. We prove…

To appear in Encyclopedia of Mathematical Physics, published by Elsevier in early 2006. Comments/corrections welcome. The article surveys topological aspects in gauge theories.

In this paper, we mainly investigate distortion and covering theorems on some classes of pluriharmonic mappings.

This is a review article on mirror symmetry and aspects of it related to the theory of modular forms. We describe this topic along its historical development and connect to some more recent results toward the end. The article is for…

In this note, we show that for any harmonic map into a non-compact symmetric space one can find naturally a "dual" harmonic map into a compact symmetric space which can be constructed from the same basic data (called "potentials" in the…

This is a survey paper on Legendrian and transversal knots for Handbook of Knot Theory.

The aim of this paper is to study some examples of exponentially harmonic maps. We study such maps firstly on flat euclidean and Minkowski spaces and secondly on Friedmann-Lema\^ itre universes. We also consider some new models of…

This survey describes some useful properties of the local homology of abstract simplicial complexes. Although the existing literature on local homology is somewhat dispersed, it is largely dedicated to the study of manifolds, submanifolds,…

We prove that polyharmonic maps of arbitrary order from complete nonparabolic Riemannian manifolds to arbitrary Riemannian manifolds must be harmonic if certain smallness and integrability conditions hold.

In this note, we investigate estimates of the Morse index for F-harmonic maps into spheres, our results extend partially those obtained in ([14]) and ([15]) for harmonic and p-harmonic maps.

We prove a regularity theorem for harmonic maps into Teichm\"uller space. More specifically, if $u$ is a harmonic map from a Riemannian domain to the metric completion of Teichm\"uller space with respect to the Weil-Petersson metric, and…

This is a survey paper that also contains some new results. It will appear in the proceedings of the AMS summer research institute on Algebraic Geometry at Santa Cruz.

In this survey we overview known results and get several new results on digraph compositions which generalize several classes of digraphs, such as quasi-transitive digraphs. After an introductory section, the paper is divided into six…

In this paper, we investigate some properties of pluriharmonic mappings defined in the unit ball. First, we discuss some geometric univalence criteria on pluriharmonic mappings, and then establish a Landau-Bloch theorem for a class of…

An exposition of the 1918 paper of Latt\`es, together with its historical antecedents, and its modern formulations and applications.

This paper is a study of harmonic maps from Riemannian polyhedra to (locally) non-positively curved geodesic spaces in the sense of Alexandrov. We prove Liouville-type theorems for subharmonic functions and harmonic maps under two different…

The survey presents the well-known Warshall's algorithm, a generalization and some interesting applications of this.

In a recent paper the first and the third authors introduced the notion of horizontal \alpha-harmonic map, with respect to a given C^1 planes distribution P_T on all R^m. The goal of this paper is to investigate compactness and quantization…

Estimating the coefficient functionals on various classes of holomorphic functions traditionally forms an important field of geometric complex analysis and its mathematical and physical applications. These coefficients reflect fundamental…