Related papers: Boundary regularity for manifold constrained $p(x)…

In this article, we investigate the regularity for certain elliptic systems without a $L^2$-antisymmetric structure. As applications, we prove some $\epsilon$-regularity theorems for weakly harmonic maps from the unit ball $B= B(m) \subset…

In the case where both the domain and target manifolds are almost Hermitian, we introduce the concept of Hermitian pluriharmonic maps. We prove that any holomorphic or anti-holomorphic map between almost Hermitian manifolds is Hermitian…

We show the regularity of, and derive a-priori estimates for (weakly) harmonic maps from a Riemannian manifold into a Euclidean sphere under the assumption that the image avoids some neighborhood of a half-equator. The proofs combine…

Let $f(z)=h(z)+\overline{g(z)}$ be a harmonic mapping of the unit disk $U$. In this paper, the sharp coefficient estimates for bounded planar harmonic mappings are established, the sharp coefficient estimates for normalized planar harmonic…

The goal of this article is to study compact quasi-Einstein manifolds with boundary. We provide boundary estimates for compact quasi-Einstein manifolds simi\-lar to previous results obtained for static and $V$-static spaces. In addition, we…

For any $n$-dimensional compact spin Riemannian manifold $M$ with a given spin structure and a spinor bundle $\Sigma M$, and any compact Riemannian manifold $N$, we show an $\epsilon$-regularity theorem for weakly Dirac-harmonic maps . As a…

In this note we shall show that the sectional curvature of a harmonic manifold is bounded on both sides. In fact we shall give a pinching constant for all harmonic manifolds. We shall use the imbedding theorem for harmonic manifolds proved…

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…

Asymptotic behavior of energy of a harmonic map defined on an asymptotically hyperbolic manifold is considered. Using the growth of energy, we show that a harmonic map defined on some asymptotically hyperbolic manifolds has to be constant…

In this paper, we develop the infinitesimal geometry of the limit spaces of compact Riemannian manifolds with boundary, where we assume lower bounds on the sectional curvatures of manifolds and boundaries and the second fundamental forms of…

In this article we introduce a natural extension of the well-studied equation for harmonic maps between Riemannian manifolds by assuming that the target manifold is equipped with a connection that is metric but has non-vanishing torsion.…

We prove a boundary Harnack principle in Lipschitz domains with small constant for fully nonlinear and $p$-Laplace type equations with a right hand side, as well as for the Laplace equation on nontangentially accessible domains under extra…

We study harmonic and quasi-harmonic discs in metric spaces admitting a uniformly local quadratic isoperimetric inequality for curves. The class of such metric spaces includes compact Lipschitz manifolds, metric spaces with upper or lower…

We study biharmonic maps between Riemannian manifolds with finite energy and finite bi-energy. We show that if the domain is complete and the target of non-positive curvature, then such a map is harmonic. We then give applications to…

We study regularity of minimizing $p$-harmonic maps $u \colon B^3 \to \mathbb{S}^3$ for $p$ in the interval $[2,3]$. For a long time, regularity was known only for $p = 3$ (essentially due to Morrey) and $p = 2$ (Schoen-Uhlenbeck), but…

We study polyharmonic (k-harmonic) maps between Riemannian manifolds with finite j-energies (j=1, cdots, 2k-2). We show if the domain is complete and the target is the Euclidean space, then such a map is harmonic.

The aim of this study is to analyze the properties of harmonic fields in the vicinity of rough boundaries where either a constant potential or a zero flux is imposed, while a constant field is prescribed at an infinite distance from this…

For any $n \geq 3$ and any closed manifold $\mathcal{N}$ with $\pi_{n+k}(\mathcal{N}) \neq \{0\}$ for some $k \geq 0$, we establish the existence of nontrivial $n$-harmonic maps from $\mathbb{S}^n$ into $\mathcal{N}$. When $k\geq 1$, these…

We give necessary and sufficient conditions for Riemannian maps to be biharmonic. We also define pseudo umbilical Riemannian maps as a generalization of pseudo-umbilical submanifolds and show that such Riemannian maps put some restrictions…

In this paper, we establish an improved coefficient bounds for quasiregular and elliptic harmonic mappings and using these bounds we establish Landau-Bloch type theorem for $(K,K')$-elliptic and K-quasiregular harmonic mappings in plane.…