arXiv research

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

Study finds nontrivial $n$-harmonic maps from $S^n$ to closed manifolds.

We prove local Holder continuity of quasi-n-harmonic mappings from Euclidean domains into metric spaces with non-positive curvature in the sense of Alexandrov. We also obtain global Holder continuity of such mappings from bounded Lipschitz domains.

For $n\ge 3$, let $Ω$ be a bounded domain in $R^n$ and $N$ be a compact Riemannian manifold in $R^L$ without boundary. Suppose that $u_n\in W^{1,n}(Ω,N)$ are the Palais-Smale sequences of the Dirichlet $n$-energy functional and $u_n$ converges weakly in $W^{1,n}$ to a map $u\in W^{1,n}(Ω,N)$. Then $u$ is a $n$-harmonic…

Paper studies heat flow for maps on manifolds, avoiding singularities.

Unified approach to Laplace and Steklov eigenvalues via $n$-harmonic maps.

This article studies the smoothness of conformal mappings between two Riemannian manifolds whose metric tensors have limited regularity. We show that any bi-Lipschitz conformal mapping or $1$-quasiregular mapping between two manifolds with $C^r$ metric tensors ($r > 1$) is a $C^{r+1}$ conformal (local) diffeomorphism. …

Paper studies smoothness of bi-conformal heat flow on 4-manifolds.

The paper constructs new non-trivial harmonic maps into higher-dimensional target manifolds.

Harmonic maps from S^2 to S^2 are all weakly conformal, and so are represented by rational maps. This paper presents a study of the L^2 metric gamma on M_n, the space of degree n harmonic maps S^2 -> S^2, or equivalently, the space of rational maps of degree n. It is proved that gamma is Kaehler with respect to a certa…

The paper classifies Willmore 2-spheres in $S^n$.

In this article we introduce local gauge conditions under which many curvature tensors appearing in conformal geometry, such as the Weyl, Cotton, Bach, and Fefferman-Graham obstruction tensors, become elliptic operators. The gauge conditions amount to fixing an $n$-harmonic coordinate system and normalizing the determi…

In n-dimensional Euclidean space E^n, harmonic curvatures of a non-degenerate curve defined by Özdamar and Hacisalihoğlu [4]. In this paper, We define a new type of curves called LC helix when the angle between tangent of this curve and LC parallel vector field in space form is constant. Furthermore, several characteri…

Harmonic metrics are established for SO0(n,n)-Higgs bundles on non-compact hyperbolic surfaces.

This work connects symmetries and conserved quantities in machine learning.

The article explores the mapping class group using unicellular maps and provides filtrations.

Constructs a moment map flow for isotropic maps on surfaces.

Maps are an important medium that enable people to comprehensively understand the configuration of cultural activities and natural elements over different times and places. Although massive maps are available in the digital era, how to effectively and accurately access the required map remains a challenge today. Previo…

The paper constructs biharmonic maps between spheres using polynomial maps.

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 …

Research explores real algebraic realization of round fold maps of codimension -1.

The paper derives Liouville theorems for various generalized maps on Riemannian manifolds.

This paper shows semi-equivelar toroidal maps are vertex-transitive covers.

Paper defines and studies Clairaut warped product Riemannian maps.

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

The hyperelliptic mapping class group has been studied in various contexts within topology and algebraic geometry. What makes this study tractable is that there is a surjective map from the hyperelliptic mapping class group to a mapping class group of a punctured sphere. The more general family of superelliptic mapping…

This paper constructs real algebraic maps that are topologically special generic maps.

A Reeb space is defined as the space of all the connected components of inverse images of a smooth map, which is a fundamental tool in studying smooth manifolds using generic smooth maps whose codimensions are not positive such as Morse functions, their higher dimensional versions including fold maps and general stable…

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

Characterizes a general range decreasing group homomorphism.

The paper examines $HM$-tensional and $HS$-tensional maps between Riemannian manifolds.

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

Dirac-harmonic maps are uncoupled under certain conditions.

We introduce slant Riemannian maps from Riemannian manifolds to almost Hermitian manifolds as a generalization of slant immersions, invariant Riemannian maps and anti-invariant Riemannian maps. We give examples, obtain characterizations and investigate the harmonicity of such maps. We also obtain necessary and sufficie…

Analyzes harmonic and biharmonic maps from gradient Ricci solitons.

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

In this paper, we show that one can interrelate pluriharmonic maps with para-pluriharmonic maps by means of the loop group method. As an appendix, we give examples for the interrelation between pluriharmonic maps and para-pluriharmonic maps. Moreover, we investigate the relation among CMC-surfaces by use of such maps.

The article explores constructing biharmonic and conformal biharmonic maps to spheres.

Harmonic map flow preserves almost-holomorphic maps without singularities.

Method computes harmonic and conformal maps from point clouds.

New theorem proves convergence of various discrete conformal structures to conformal maps.

Constructs harmonic maps between special geometric shapes.

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

Study isotropic Riemannian maps and helices along them.

Study on harmonic maps on weighted Riemannian foliations.

Maps and measures on surfaces link best Lipschitz and least gradient functions.

The construction of topological index maps for equivariant families of Dirac operators requires factoring a general smooth map through maps of a very simple type: zero sections of vector bundles, open embeddings, and vector bundle projections. Roughly speaking, a normally non-singular map is a map together with such a …

Paper proves existence and gives construction of Symphonic map between ellipsoids.