Related papers: On $(H,\widetilde{H})$-harmonic Maps between pseud…

It was conjectured by Eells that the only harmonic maps $f : S^3 \to S^2$ are Hopf fibrations composed with conformal maps of $S^2$. We support this conjecture by proving its validity under suitable conditions on the Hessian and the…

The goal of the present paper is to establish some kind of regularity of an energy minimizer map between Riemannian polyhedra. More precisely, we will show the h\"{o}lder continuity of local energy minimizers between Riemannian polyhedra…

In this paper, we give some rigidity results for both harmonic and pseudoharmonic maps from CR manifolds into Riemannian manifolds or Kahler manifolds. Some basicity, pluriharmonicity and Siu-Sampson type results are established for both…

We study a version of Calder\'on's problem for harmonic maps between Riemannian manifolds. By using the higher linearization method, we first show that the Dirichlet-to-Neumann map determines the metric on the domain up to a natural gauge…

Motivated by geometry processing for surfaces with non-trivial topology, we study discrete harmonic maps between closed surfaces of genus at least two. Harmonic maps provide a natural framework for comparing surfaces by minimizing…

We study a Floer-theoretic approach to harmonic maps from the two-torus into non-flat K\"ahler manifolds. Building on the complex-regularized polysymplectic (CRPS) formalism of [BF24], which provides a Hamiltonian description of harmonic…

We introduce holomorphic Riemannian maps between almost Hermitian manifolds as a generalization of holomorphic submanifolds and holomorphic submersions, give examples and obtain a geometric characterization of harmonic holomorphic…

Every oriented 4-manifold admits a folded symplectic structure, which in turn determines a homotopy class of compatible almost complex structures that are discontinuous across the folding hypersurface ("fold") in a controlled fashion. We…

For a fixed smooth map $u_0$ between two Riemann surfaces $\Sigma$ and $S$ with non-zero degree, we consider the energy function on Teichm\"uller space $\mc{T}$ of $\Sigma$ that assigns to a complex structure $t\in \mc{T}$ on $\Sigma$ the…

The main aim of this paper is to prove the existence of certain proper weakly $r$-harmonic ($ES-r$-harmonic) maps. We construct critical points which belong to a family of rotationally symmetric maps $\varphi_a : B^n \to \mathbb{S}^n$,…

H-holomorphic maps are a parameter version of J-holomorphic maps into contact manifolds. They have arisen in efforts to prove the existence of higher--genus holomorphic open book decompositions and efforts to prove the existence of finite…

Let $\pi:\mc{X}\to \mc{T}$ be Teichm\"uller curve over Teichm\"uller space $\mc{T}$, such that the fiber $\mc{X}_z=\pi^{-1}(z)$ is exactly the Riemann surface given by the complex structure $z\in \mc{T}$. For a fixed Riemannian manifold $M$…

We prove a general comparison result for homotopic finite $p$-energy $C^{1}$ $p$-harmonic maps $u,v:M\to N$ between Riemannian manifolds, assuming that $M$ is $p$-parabolic and $N$ is complete and non-positively curved. In particular, we…

Consider the cotangent bundle of a Riemannian manifold $(M,g)$ of dimension 2 or more, endowed with a twisted symplectic structure defined by a closed weakly exact 2-form $\sigma$ on $M$ whose lift to the universal cover of $M$ admits a…

We establish a geometric inequality relating the Dirichlet energy $E_1(f)$ and the bienergy $E_2(f)$ of smooth maps \[ f : (M,g) \to (\overline{M},\overline{g}) \] between Riemannian manifolds. Assume that $(M,g)$ is a compact, connected…

We characterize general pseudo-harmonic morphisms from a Riemannian manifold to a Hermitian manifold as pseudo horizontally weakly conformal maps with an additional property. We study to what extent we can (locally) describe these…

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…

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…

We construct a closed Riemannian manifold $(N,h)$ and a sequence of $\alpha$-harmonic maps from $S^2$ into $N$ with uniformly bounded energy such that the energy identity for this sequence is not true.

Harmonic morphisms are maps between Riemannian manifolds that pull back harmonic functions to harmonic functions. These maps are characterized as horizontally weakly conformal harmonic maps and they have many interesting links and…