arXiv research

Study of moduli spaces for special harmonic maps from projective line to quadrics.

Introduces Einstein-Hermitian connections on symplectic generalized Kähler manifolds.

A harmonic map from a Riemannian manifold into a Grassmannian manifold is characterized by a vector bundle, a space of sections of this bundle and a Laplace operator. We apply our main theorem, itself a generalization of a Theorem of Takahashi, to generalize the theory of do Carmo and Wallach and to describe the moduli…

This paper establishes a correspondence between Einstein-Hermitian metrics and stability for generalized holomorphic vector bundles over symplectic type generalized Kahler manifolds.

Let $X$ be a smooth projective variety over $\mathbb C$. We prove that a twisted Higgs vector bundle $(\calE\, ,θ)$ on $X$ admits an Einstein--Hermitian connection if and only if $(\calE\, ,θ)$ is polystable. A similar result for twisted vector bundles (no Higgs fields) was proved by S. Wang in \cite{Wa}. Our approach …

Introduces new equations linking Kähler-Einstein and Hermitian-Yang-Mills theories.

We give a mathematical exposition of the Page metric, and introduce an efficient coordinate system for it. We carefully examine the submanifolds of the underlying smooth manifold, and show that the Page metric does not have positive holomorphic bisectional curvature. We exhibit a holomorphic subsurface with flat normal…

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.

Paper proves existence of smooth nontrivial Dirac-harmonic maps.

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

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

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…

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

Constructs harmonic maps between special geometric shapes.

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

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

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

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.

Study on bi-$f$-harmonic curves and hypersurfaces extending harmonic and biharmonic concepts.

The paper examines stability of subelliptic harmonic maps with potential.

Extends energy gap result for high-energy harmonic maps.

Survey on Higgs bundles via harmonic maps and their role in non-abelian Hodge correspondence.

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

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,…

Extends Fatou theorem to bounded harmonic maps.

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.

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

Paper generalizes Schwarz Lemma for VT harmonic maps with conditions.

The paper studies harmonic identity maps on Riemannian manifolds.

It is well known that any 4-dimensional hyperkahler metric with two commuting Killing fields may be obtained explicitly, via the Gibbons-Hawking Ansatz, from a harmonic function invariant under a Killing field on R^3. In this paper, we find all selfdual Einstein metrics of nonzero scalar curvature with two commuting Ki…

Study of generalized harmonic morphisms and biharmonic maps.

The study connects harmonic mappings to Ricci solitons.

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

Study sesqui-harmonic map flow from Riemannian surfaces

Method computes harmonic and conformal maps from point clouds.

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

New structures help create harmonic maps.