arXiv research

Paper approximates fractional harmonic maps with numerical methods.

Uniform small energy regularity for fractional geometric problems proved.

Minimal harmonic maps proved for specific manifolds.

Study on fractional mass for codimension-two currents, proving equi-coercivity and Γ-convergence.

Study fractional perimeter asymptotics on Riemannian manifolds as $s$ approaches 0.

We develop a regularity theory for extremal knots of scale invariant knot energies defined by J. O'hara in 1991. This class contains as a special case the Möbius energy. For the Möbius energy, due to the celebrated work of Freedman, He, and Wang, we have a relatively good understanding. Their approch is crucially based…

We consider minimizing harmonic maps $u$ from $Ω\subset \mathbb{R}^n$ into a closed Riemannian manifold $\mathcal{N}$ and prove: (1) an extension to $n \geq 4$ of Almgren and Lieb's linear law. That is, if the fundamental group of the target manifold $\mathcal{N}$ is finite, we have \[ \mathcal{H}^{n-3}(\textrm{sing } …

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…

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 examines stability of harmonic maps on specific manifolds.

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

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.

Methods from the geometry of nonholonomic manifolds and Lagrange-Finsler spaces are applied in fractional calculus with Caputo derivatives and for elaborating models of fractional gravity and fractional Lagrange mechanics. The geometric data for such models are encoded into (fractional) bi-Hamiltonian structures and as…

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.

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.

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"…