Related papers: Convergence of harmonic maps

We study the existence of harmonic maps and Dirac-harmonic maps from degenerating surfaces to non-positive curved manifold via the scheme of Sacks and Uhlenbeck. By choosing a suitable sequence of $\alpha$-(Dirac-)harmonic maps from a…

Is a sequence of Riemannian manifolds with positive scalar curvature, satisfying some conditions to keep the sequence reasonable, compact? What topology should one use for the convergence and what is the regularity of the limit space? In…

The harmonic map energy of a map from a closed, constant-curvature surface to a closed target manifold can be seen as a functional on the space of maps and domain metrics. We consider the gradient flow for this energy. In the absence of…

We study harmonic and biharmonic maps from gradient Ricci solitons. We derive a number of analytic and geometric conditions under which harmonic maps are constant and which force biharmonic maps to be harmonic. In particular, we show that…

We study compact complex 3-manifolds admitting holomorphic Riemannian metrics. We prove a uniformization result: up to a finite unramified cover, such a manifold admits a holomorphic Riemannian metric of constant sectionnal curvature.

We show that the Korevaar-Schoen limit of the sequence of equivariant harmonic maps corresponding to a sequence of irreducible $SL_2({\mathbb C})$ representations of the fundamental group of a compact Riemannian manifold is an equivariant…

In this short note we study nonexistence result of biharmonic maps from a complete Riemannian manifold into a Riemannian manifold with nonpositive sectional curvature. Assume that $\phi:(M,g)\to (N, h)$ is a biharmonic map, where $(M, g)$…

The Teichm\"uller harmonic map flow is a gradient flow for the harmonic map energy of maps from a closed surface to a general closed Riemannian target manifold of any dimension, where both the map and the domain metric are allowed to…

Within the framework of balayage spaces (the analytical equivalent of nice Hunt processes), we prove equicontinuity of bounded families of harmonic functions and apply it to obtain criteria for compactness of potential kernels.

We prove a codimension reduction and congruence theorem for compact $n$-dimensional submanifolds of $\mathbb{S}^{n+p}$ that admit a mean convex isometric embedding into $\mathbb{S}^{n+1}_+$ using a Reilly type formula for space forms.

We show that on any Riemannian manifold with H\"older continuous metric tensor, there exists a $p$-harmonic coordinate system near any point. When $p = n$ this leads to a useful gauge condition for regularity results in conformal geometry.…

A subclass of complex-valued close-to-convex harmonic functions that are univalent and sense-preserving in the open unit disc is investigated. The coefficient estimates, growth results, area theorem, boundary behavior, convolution and…

Existence of an infinite sequence of harmonic maps between spheres of certain dimensions was proven by Bizon and Chmaj. This sequence shares many features of the Bartnik-McKinnon sequence of solutions to the Einstein-Yang-Mills equations as…

We already saw in [A1] that the space of dynamically marked rational maps can be identified to a subspace of the space of covers between trees of spheres on which there is a notion of convergence that makes it sequentially compact. In the…

In this paper, we study biharmonic hypersurfaces in Einstein manifolds. Then, we determine all the biharmonic hypersurfaces in irreducible symmetric spaces of compact type which are regular orbits of commutative Hermann actions of…

Motivated by a question of Tsai-Tsui-Wang, we consider the rigidity of map from manifolds with positive Ricci curvature to manifolds with positive sectional curvature. We show that if the Ricci curvature of the domain dominates that of the…

In this paper, we mainly derive monotonicity formula of generalized map using conservation law, including $\phi$-$F$ harmonic map coupled with $\phi$-$F$ symphonic map with $m$ form and potential from metric measure space, $ p $ harmonic…

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…

Characterizations for Riemannian submersions to be harmonic or biharmonic are shown. Examples of biharmonic but not harmonic Riemannian submersions are shown.

Let $\Sigma$ be a compact oriented surface and $N$ a compact K\"ahler manifold with nonnegative holomorphic bisectional curvature. For a solution of harmonic map flow starting from an almost-holomorphic map $\Sigma \to N$ (in the energy…