Related papers: Stability for $ F $ harmonic map with two form and…
In this paper, we mainly consider the stability of $ \Phi_{S, F,H} $ harmonic map and $ \Phi_{T,F,H} $ harmonic map from or into $ \Phi $-SSU manifold. We mainly consider the stability of $ \Phi_{S, F,H} $ harmonic map and $ \Phi_{T,F,H} $…
In this paper, we investigate the stability problem of subelliptic harmonic maps with potential. First, we derive the first and second variation formulas for subelliptic harmonic maps with potential. As a result, it is proved that a…
In this paper, we motivate and define $\Phi$-energy density, $\Phi$-energy, $\Phi$-harmonic maps and stable $\Phi$-harmonic maps. Whereas harmonic maps or $p$-harmonic maps can be viewed as critical points of the integral of $\sigma_1$ of a…
The first result in this study is a non-existence theorem for $\alpha-$harmonic mappings. Additionally, a direct connection between the $\alpha-$ harmonic and harmonic maps is made possible via conformal deformation. Second, the instability…
In this paper, we study the stability problem of exponentially subelliptic harmonic maps from sub-Riemannian manifolds to Riemannian manifolds. We derive the rst and second variation formulas for exponentially subelliptic harmonic maps, and…
In this paper, we motivate and extend the study of harmonic maps or $\Phi_{(1)}$-harmonic maps (cf [15], Remark 1.3 (iii)), $\Phi$-harmonic maps or $\Phi_{(2)}$-harmonic maps (cf. [24], Remark 1.3 (v)), and explore geometric properties of…
Both bi-harmonic map and $f$-harmonic map have nice physical motivation and applications. In this paper, by combination of these two harmonic maps, we introduce and study $f$-bi-harmonic maps as the critical points of the $f$-bi-energy…
We study a second order differential equation corresponding to rotationally symmetric $F$-harmonic maps between certain noncompact manifolds. We show unique continuation and Liouville's type theorems for positive solutions. Asymptotic…
In this paper, we discuss the associated family of harmonic maps $\mathcal{F}: M \rightarrow G/K$ from a Riemann surface $M$ into inner symmetric spaces of compact or non-compact type which are either algebraic or totally symmetric. These…
We prove that, in general, given a $p$-harmonic map $F:M\to N$ and a convex function $H:N\to\mathbb{R}$, the composition $H\circ F$ is not $p$-subharmonic. By assuming some rotational symmetry on manifolds and functions, we reduce the…
In this paper, we extend the definition of p-harmonic and p-biharmonic maps between Riemannian manifolds. We present some new properties for the generalized stable p-harmonic maps.
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…
In this paper, we first study the $\alpha-$energy functional, Euler-Lagrange operator and $\alpha$-stress energy tensor. Second, it is shown that the critical points of $\alpha-$ energy functional are explicitly related to harmonic maps…
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…
This note introduces an extension to the definition of symphonic maps, denoted as $\varphi:(M,g)\longrightarrow(N,h)$, by exploring variations in the bi-energy functional associated with the pullback metric $\varphi^*h$ between two…
In this paper, we study stability for harmonic foliations on locally conformal K\"ahler manifolds with complex leaves. We also discuss instability for harmonic foliations on compact submanifolds immersed in Euclidean spaces and compact…
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…
For any smooth compact manifold $W$ of dimension at least two we prove that the classifying spaces of its group of diffeomorphisms which fix a set of $k$ points or $k$ embedded disks (up to permutation) satisfy homology stability. The same…
In this paper, we obtained Liouville theorem for $ \phi $-$F$-symphonic map , $ \phi $-$F$-harmonic map and $ \phi $-$\Phi_{S, p, \varepsilon}$ harmonic map with free boundary on metric measure space.
We introduce the {\em $\mu$-topological stability}. This is a type of stability depending on the measure $\mu$ different from the set-valued approach \cite{lm}. We prove that the map $f$ is $m_p$-topologically stable if and only if $p$ is a…