arXiv research

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

Paper proves energy identity and no-neck property for special harmonic maps.

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

Classifies low energy maps from curved surfaces into spheres.

Study shows only rotations can be approximated by Ginzburg-Landau critical points.

The paper extends energy identities and neck existence for ε-harmonic maps.

$α$-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 …

This study recovers electromagnetic parameters on boundaries from impedance and admittance data.

Proves theorem for Riemannian manifolds, extending previous work.

Study of critical points in Ginzburg-Landau approximation with stability results.

We study a variational Ginzburg-Landau type model depending on a small parameter $\varepsilon>0$ for (tangent) vector fields on a $2$-dimensional Riemannian manifold $S$. As $\varepsilon\to 0$, these vector fields tend to have unit length so they generate singular points, called vortices, of a (non-zero) index if the g…

The paper proves geodesics and conic sections are length-minimizing under specific metrics.

The study classifies warped products with harmonic curvature on surfaces, showing two possibilities for the metric.

The paper studies Dirac operators and their solutions concentrating near singular sets.

Paper proves Liouville theorems for harmonic functions under specific curvature bounds.

In this paper we investigate the existence of a solution to the Poisson equation on complete manifolds with positive spectrum and Ricci curvature bounded from below. We show that if a function $f$ has decay $f=O(r^{-1-\varepsilon})$ for some $\varepsilon >0,$ where $r$ is the distance function to a fixed point, then t…

Let $f\colon \mathbb{S}^1\rightarrow G$ be a surjective map from the standard unit circle to a graph $G$ such that the pre-image of each point has diameter less than $\varepsilon$. If $\varepsilon$ is small enough, does $f$ split as a free factor in $π_1(G)$?

The study finds critical points of Yang-Mills-Higgs energy on 3-manifolds.

We study the asymptotic Dirichlet problem for $\mathcal{A}$-harmonic functions on a Cartan-Hadamard manifold whose radial sectional curvatures outside a compact set satisfy an upper bound $K(P)\le - \frac{1+\varepsilon}{r(x)^2 \log r(x)}$ and a pointwise pinching condition $|K(P)|\le C_K |K(P')|$ for some const…

Study on harmonic maps on weighted Riemannian foliations.

Algorithm finds real line mapping from points under ordinal constraints.

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.

A new diffusion method approximates Schrödinger bridge with improved convergence.

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.

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…

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

The paper examines stability of subelliptic harmonic maps with potential.

Constructs new connections with finite energy in 4D, preserving gauge equivalence and curvature properties.

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.