arXiv research

This paper investigates analytic properties of maps between hyperbolic surfaces, focusing on best Lipschitz maps and geodesic laminations.

Let $p$ be an even positive integer and $U_p(H)$ be the Banach-Lie group of unitary operators $u$ which verify that $u-1$ belongs to the $p$-Schatten ideal $B_p(H)$. Let ${\cal O}$ be a smooth manifold on which $U_p(H)$ acts transitively and smoothly. Then one can endow ${\cal O}$ with a natural Finsler metric in terms…

The paper studies a special Grassmannian space and shows it's an orbit of a unitary group.

Let $U_c(H)={u: u is unitary and u-1 is compact}$ stand for the unitary Fredholm group. We prove the following convexity result. Denote by $d_\infty$ the rectifiable distance induced by the Finsler metric given by the operator norm in $U_c(H)$. If $u_0,u_1,u\in U_c(H)$ and the geodesic $β$ joining $u_0$ and $u_1$ in $U…

Study on harmonic maps on weighted Riemannian foliations.

Study cohomology classes related to harmonic maps on submersions.

The paper proves nonexistence of harmonic and bi-harmonic maps under specific conditions.

Dirac-harmonic maps are uncoupled under certain conditions.

Extends p-harmonic map theory for new properties.

Analyzes harmonic and biharmonic maps from gradient Ricci solitons.

Study on harmonic maps between cones, linking degrees to graph Laplacian eigenvalues.

Study heat flow for half-harmonic maps and harmonic maps with free boundary.

Study existence of harmonic and Dirac-harmonic maps from degenerating surfaces.

The paper constructs gluing maps for harmonic maps between Riemannian manifolds.

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 functional $\frac{1}{2}\int_M f|τ(φ)|^2dv_{g}$. This class of maps generalizes both …

$\infty$-Harmonic maps are a generalization of $\infty$-harmonic functions. They can be viewed as the limiting cases of p-harmonic maps as p goes to infinity. In this paper, we give complete classifications of linear and quadratic $\infty$-harmonic maps from and into a sphere, quadratic $\infty$-harmonic maps between E…

Let $L^2$ be the Lebesgue space of square-integrable functions on the unit circle. We show that the injectivity problem for Toeplitz operators is linked to the existence of geodesics in the Grassmann manifold of $L^2$. We also investigate this connection in the context of restricted Grassmann manifolds associated to $p…

Constructs harmonic maps between special geometric shapes.

The paper proves a Liouville theorem for specific harmonic maps with free boundary.

Study cohomology classes related to $n$-harmonic morphisms and $F$-harmonic maps.

Harmonic maps studied in sub-Riemannian geometry for Lie groups.

The paper studies geometric properties of $Φ_{(3)}$-harmonic maps and proves Liouville type results.

The paper examines stability of harmonic maps on specific manifolds.

J. Eells and L. Lemaire introduced k-harmonic maps, and Wang Shaobo showed the first variational formula. When, k=2, it is called biharmonic maps (2-harmonic maps). There have been extensive studies in the area. In this paper, we consider the relationship between biharmonic maps and k-harmonic maps, and show non-existe…

$α$-Dirac-harmonic maps are variations of Dirac-harmonic maps, analogous to $α$-harmonic maps that were introduced by Sacks-Uhlenbeck to attack the existence problem for harmonic maps from surfaces. For $α>1$, the latter are known to satisfy a Palais-Smale condtion, and so, the technique of Sacks-Uhlenbeck consists in …

Finite energy solutions of 4-harmonic and ES-4-harmonic maps are trivial.

The paper examines stability of subelliptic harmonic maps with potential.

The paper studies maps from pseudo-Hermitian to Kähler manifolds, proving harmonic map properties.

Extends Fatou theorem to bounded harmonic maps.

We propose a new notion called \emph{infinity-harmonic maps}between Riemannain manifolds. These are natural generalizations of the well known notion of infinity harmonic functions and are also the limiting case of $p$% -harmonic maps as $p\to \infty$. Infinity harmoncity appears in many familiar contexts. For example,…

The paper explores unique continuation properties for polyharmonic maps between Riemannian manifolds.

The paper proves a Liouville theorem for a specific type of harmonic maps on foliated manifolds.

Paper generalizes Schwarz Lemma for VT harmonic maps with conditions.

Study on stability of harmonic maps with sub-Riemannian geometry.

The paper studies harmonic identity maps on Riemannian manifolds.

Study sesqui-harmonic map flow from Riemannian surfaces

Sharp inequality for $p$-harmonic maps with new optimal constant.

Method computes harmonic and conformal maps from point clouds.

The paper characterizes harmonic maps and studies their properties on Riemannian manifolds.

New $\varepsilon$-harmonic maps of low degree are rigid under certain energy bounds.

Study proves existence of non-trivial harmonic map flows to hemispheres.

Develops a framework for generating harmonic maps from a unit ball to a sphere.

New rigidity estimate derived via harmonic map flow.

J. Eells and L. Lemaire introduced k-harmonic maps, and Wang Shaobo showed the first variational formula. When, k=2, it is called biharmonic maps (2-harmonic maps). There have been extensive studies in the area. In this paper, We study k-harmonic immersion into a sphere, and get the rerationship between radious and "k"…

In the paper, we study variation formulas for transversally harmonic maps and bi-harmonic maps, respectively. We also study the transversal Jacobi field along a map and give several relations with infinitesimal automorphisms.

Quantifies uniqueness of conformal-harmonic maps on 4-manifolds.

The paper explores $\alpha-$harmonic maps and their stability, proving key properties and conditions.

Harmonic maps between pinched Hadamard surfaces are quasi-conformal.