Related papers: Transverse Measures and Best Lipschitz and Least G…

We describe work on solutions of certain non-divergence type and therefore non-variational elliptic and parabolic systems on manifolds. These systems include Hermitian and affine harmonics which should become useful tools for studying…

For a compact riemannian manifold of negative curvature, the geodesic foliation of its unit tangent bundle is independent of the negatively curved metric, up to Holder bicontinuous homeomorphism. However, the riemannian metric defines a…

On non-K\"ahler manifolds the notion of harmonic maps is modified to that of Hermitian harmonic maps in order to be compatible with the complex structure. The resulting semilinear elliptic system is {\it not} in divergence form. The case of…

We investigate shrinking maps from a cusped hyperbolic surface into the moduli space of closed Riemann surfaces. For such a map and its lift to the Teichm\"uller space, we consider whether they are quasi-isometric embeddings with respect to…

In this paper we study an energy of maps between almost Hermitian manifolds for which pseudo-holomorphic maps are global minimizers. We derive its Euler-Lagrange equation, the $\bar{\partial}$-harmonic map equation, and show that it…

In this paper, we first obtain an $L^q$ gradient estimate for $p$-harmonic maps, by assuming the target manifold supporting a certain function, whose gradient and Hessian satisfy some analysis conditions. From this $L^q$ gradient estimate,…

In this short note, we show that, in any given metric space, every Lipschitz open-map image of every subset of a given metric space whose boundary is Hausdorff-null is Hausdorff-measurable with respect to the same dimension. The main…

Motivated by the rich theory of harmonic maps from a 2-sphere, we study biharmonic maps from a 2-sphere in this paper. We first derive biharmonic equation for rotationally symmetric maps between rotationally symmetric 2-manifolds. We then…

An existence result is shown for the asymptotic Dirichlet problem for harmonic maps from the product of the hyperbolic planes to the hyperbolic space, where the Dirichlet data is given on the distinguished boundary (the product of the…

The Teichm\"uller harmonic map flow, introduced in [9], evolves both a map from a closed Riemann surface to an arbitrary compact Riemannian manifold, and a constant curvature metric on the domain, in order to reduce its harmonic map energy…

We give conditions on the Lee vector field of an almost Hermitian manifold such that any holomorphic map from this manifold into a (1,2)-symplectic manifold must satisfy the fourth-order condition of being biharmonic, hence generalizing the…

Given a reductive representation $\rho: \pi_1(S)\rightarrow G$, there exists a $\rho$-equivariant harmonic map $f$ from the universal cover of a fixed Riemann surface $\Sigma$ to the symmetric space $G/K$ associated to $G$. If the Hopf…

We study the homotopical minimal measures for positive definite autonomous Lagrangian systems. Homotopical minimal measures are action-minimizers in their homotopy classes, while the classical minimal measures (Mather measures) are…

We introduce a hyperbolic Gauss map into the Poincare disk for any surface in H^2xR with regular vertical projection, and prove that if the surface has constant mean curvature H=1/2, this hyperbolic Gauss map is harmonic. Conversely, we…

We show that in all homotopy classes of mappings from complex projective space to Riemannian manifolds, the infimum of the energy is proportional to the infimal area in the homotopy class of mappings of the 2-sphere which represents the…

In this paper, we introduce an asymmetric metric on the space of marked Euclidean triangles, and we prove several properties of this metric, including two equivalent definitions of this metric, one of them comparing ratios of functions of…

A measured laminations on the universal hyperbolic solenoid $\S$ is, by our definition, a leafwise measured lamination with appropriate continuity for the transverse variations. An earthquakes on theuniversal hyperbolic solenoid $\S$ is…

Here we study what we call bounded rough Riemannian metrics $(M,g)$, which are positive definite, symmetric tensors on each tangent space, $T_pM$, which are bounded and measurable as functions in coordinates. This is enough structure to…

This article studies the harmonicity of vector fields on Riemannian manifolds, viewed as maps into the tangent bundle equipped with a family of Riemannian metrics. Geometric and topological rigidity conditions are obtained, especially for…

We explore the interplay between different definitions of distortion for mappings $f\colon X\to \mathbb{R}^2$, where $X$ is any metric surface, meaning that $X$ is homeomorphic to a domain in $\mathbb{R}^2$ and has locally finite…