arXiv research

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

Study harmonic surfaces in 3D space, proving superposition principle.

Harmonic basis vector fields on surfaces

The notion of a generalized harmonic inverse mean curvature surface in the Euclidean four-space is introduced. A backward Bäcklund transform of a generalized harmonic inverse mean curvature surface is defined. A Darboux transform of a generalized harmonic inverse mean curvature surface is constructed by a backward Bäck…

Harmonic maps between pinched Hadamard surfaces are quasi-conformal.

Study Liouville action for harmonic maps between Riemann surfaces.

The study derives formulas for functionals on surface with boundary under harmonic Ricci flow.

Unified study of harmonic maps between pseudo-Riemannian surfaces.

A formula connects discrete harmonic surfaces to holomorphic functions.

The Weierstrass representation for minimal surfaces in $\mathbb{R}^3$ provides a flexible method for constructing minimal surfaces of arbitrary genus. The topological limitations of minimal surfaces interfere with this providing a more general geometric modeling tool. Minimal surfaces lie in the larger class of harmoni…

Extends harmonic maps compactification to punctured Riemann surfaces.

Study harmonic metrics on Higgs bundles on non-compact Riemann surfaces.

Method computes harmonic and conformal maps from point clouds.

Extends harmonic map theory to arbitrary surfaces.

We define two transforms between non-conformal harmonic maps from a surface into the 3-sphere. With these transforms one can construct, from one such harmonic map, a sequence of harmonic maps. We show that there is a correspondence between non-conformal harmonic maps into the 3-sphere, $H$-surfaces in Euclidean 3-space…

The study examines harmonic forms on almost Hermitian manifolds and complex surfaces.

In this note we demonstrate how the analogy between the harmonic Gauss map of a constant mean curvature surface and the harmonic conformal Gauss map of a Willmore surface can be used to obtain results on Willmore surfaces.

We will investigate the local geometry of the surfaces in the $7$-dimensional Euclidean space associated to harmonic maps from a Riemann surface $Σ$ into $S^6$. By applying methods based on the use of harmonic sequences, we will characterize the conformal harmonic immersions $\varphi:Σ\to S^6$ whose associated immersio…

We discuss non-conformal harmonic surfaces in $R^3$ with prescribed ($\pm$)transforms, and we get a representation formula for non-conformal harmonic surfaces in $R^3$.

The study characterizes surfaces with specific harmonic properties in pseudo-conformal geometry.

New proof of timelike minimal surfaces using split-harmonic maps.

Optimal discrete harmonic maps between hyperbolic surfaces are found via minimizing energy.

The study examines stability of fibres on Hopf surfaces as harmonic maps and minimal surfaces.

One-harmonic maps from a curved surface to hyperbolic plane have specific interior properties.

Study Lorentz harmonic maps and spacelike surfaces in anti-de Sitter space.

Study sesqui-harmonic map flow from Riemannian surfaces

We prove that the distortion function of the Gauss map of a harmonic surface coincides with the distortion function of the surface. Consequently, Gauss map of a harmonic surface is ${\mathcal{K}}$ quasiregular if and only if the surface is ${\mathcal{K}}$ quasiregular, provided that the Gauss map is regular or what is …

Embedded minimal surfaces of finite total curvature in $\mathbb{R}^3$ are reasonably well understood: From far away, they look like intersecting catenoids and planes, suitably desingularized. We consider the larger class of harmonic embeddings in $\mathbb{R}^{3}$ of compact Riemann surfaces with finitely many punctures…

Study on isoperimetric inequalities and regularity of $A$-harmonic functions on surfaces.

A new method splits surface flow discretizations into streamfunctions and harmonic fields.

The study constructs equivariant harmonic maps into symmetric spaces with applications to Willmore surfaces.

Constructs Lorentzian harmonic maps and associated timelike surfaces.

Proves open Riemann surfaces can be embedded into 4D space.

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

Study on infinite energy maps from surfaces to CAT(0) spaces.

The paper studies constant harmonic mean curvature surfaces in Schwarzschild spaces, proving they foliate the space.

Study on harmonic maps from surfaces with energy bounds and neck domains.

Study spectral distribution of twisted Laplacian on high genus hyperbolic surfaces.

P. Baird and the second author studied harmonic morphisms from a three-dimensional simply-connected space form to a surface and obtained a complete local and global classification of them. In this paper, we obtain a description of all harmonic morphisms from any three-dimensional Euclidean and spherical space form to a…

Harmonic maps intersect all minimal surfaces with bounded curvature.

We relate the existence problem of harmonic maps into $S^2$ to the convex geometry of $S^2$. On one hand, this allows us to construct new examples of harmonic maps of degree 0 from compact surfaces of arbitrary genus into $S^2$. On the other hand, we produce new example of regions that do not contain closed geodesics (…

Study of harmonic Riemannian submersions from 3D geometries.

Study on harmonic forms on K3 surfaces converging to a flat 4D orbifold.

The paper proves a factorization theorem for harmonic maps between Riemann surfaces and manifolds.

Study bounds on harmonic forms in hyperbolic 3-manifolds using Thurston norm and minimal surfaces.

Survey of Willmore surfaces in spheres using DPW method.

Study timelike minimal surfaces in Heisenberg group using harmonic maps.

New approach to heat flow for half-harmonic maps, related to minimal surfaces.