arXiv research

Classifies $π_1$-injective maps between non-compact surfaces.

Maps between non-compact surfaces can have geometric kernels under certain conditions.

Harmonic maps between pinched Hadamard surfaces are quasi-conformal.

Unified study of harmonic maps between pseudo-Riemannian surfaces.

Bi-geodesic mappings preserve distances on hyperbolic surfaces with boundaries.

The paper derives Gauss-Bonnet formulas for mappings between surfaces with boundary.

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

Biharmonic maps between surfaces are studied in this paper. We compute the bitension field of a map between surfaces with conformal metrics in complex coordinates. As applications, we show that a linear map from Euclidean plane into $(\mathbb{R}^2, σ^2dwd\bar w)$ is always biharmonic if the conformal factor $σ$ is bi-a…

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…

We show that any isomorphism between mapping class groups of orientable infinite-type surfaces is induced by a homeomorphism between the surfaces. Our argument additionally applies to automorphisms between finite-index subgroups of these `big' mapping class groups and shows that each finite-index subgroup has finite ou…

Study big mapping class groups and their co-Hopfian property, finding new examples and proving injective homomorphisms results.

Homomorphisms between pure mapping class groups are classified for certain genus surfaces.

The paper studies optimal maps between hyperbolic surfaces, focusing on their rigidity and obstructions.

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

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.

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

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

Finding surface mappings with least distortion arises from many applications in various fields. Extremal Teichmüller maps are surface mappings with least conformality distortion. The existence and uniqueness of the extremal Teichmüller map between Riemann surfaces of finite type are theoretically guaranteed [1]. Rece…

The paper classifies holomorphic maps between Riemann surface configuration spaces.

Let $F',F$ be any two closed orientable surfaces of genus $g'>g\ge 1$, and $f:F\to F$ be any pseudo-Anosov map. Then we can "extend" $f$ to be a pseudo-Anosov map $f':F'\to F'$ so that there is a fiber preserving degree one map $M(F',f')\to M(F,f)$ between the hyperbolic surface bundles. Moreover the extension $f'$ can…

Study Gauss maps of surfaces in Heisenberg group using hyperbolic geometry.

The paper studies harmonic maps between surfaces homotopic to a covering map, proving uniqueness and injectivity of Hopf differential.

The paper extends a method for numerical conformal mappings to surfaces using Laplace-Beltrami equations.

We study singularities of constant positive Gaussian curvature surfaces and determine the way they bifurcate in generic 1-parameter families of such surfaces. We construct the bifurcations explicitly using loop group methods. Constant Gaussian curvature surfaces correspond to harmonic maps, and we examine the relations…

New map connects stability conditions to Teichmüller space.

We construct new monomorphisms between mapping class groups of surfaces. The first family of examples injects the mapping class group of a closed surface into that of a different closed surface. The second family of examples are defined on mapping class groups of once-punctured surfaces and have quite curious behaviour…

The paper defines when surfaces are homotopy equivalent to graphs and explores their mapping class groups.

Unique geodesics selected by energy minimization in Teichmüller space.

In this note we give a simple relation between conformal mapping and the first eigenvalue of Laplacian for surfaces in Euclidean spaces.

The paper classifies homomorphisms between braid groups and mapping class groups.

Maps between surfaces have degree constraints based on their Euler characteristics.

Study sesqui-harmonic map flow from Riemannian surfaces

In this note, we prove a Schwarz-Pick type lemma for minimal maps between negatively curved Riemannian surfaces. More precisely, we prove that if $f:M \to N$ is a minimal map with bounded Jacobian between two complete negatively curved Riemann surfaces M and N whose sectional curvatures $σ_M$ and $σ_N$ satisfy $infσ_M …

Study bounds topological entropy of maps on surfaces with punctures based on mapping torus homology.

The paper shows compatibility between two quantum maps for surfaces and 3-manifolds.

The study examines surfaces in isotropic space with specific Gauss map properties.

Embedding calculus proves convergence for surfaces.

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.

We show that to every maximal surface with conelike singularities in Lorentz-Minkowski space $\mathbb{L}^3$ that can be locally represented as the graph of a smooth function, there exists a corresponding timelike minimal surface in $\mathbb{L}^3$. There exists a linear transformation between such a maximal surface and …

Minimal maps from surfaces to torus found for various genus values.

A new simple proof for surface map degree inequality.

We study forgetful maps between Deligne-Mostow moduli spaces of weighted points on P^1, and classify the forgetful maps that extend to a map of orbifolds between the stable completions. The cases where this happens include the Livné fibrations and the Mostow/Toledo maps between complex hyperbolic surfaces. They also in…

The paper studies branched surfaces and their properties.

Lipschitz mappings found between Riemann surfaces with specific properties.

Geodesics count exponentially between triangulations of surfaces with enough topology.

We prove that every injective simplicial map $\mathcal{F}(S) \to \mathcal{F}(S')$ between flip graphs is induced by a subsurface inclusion $S\to S'$, except in finitely many cases. This extends a result of Korkmaz--Papadopoulos which asserts that every automorphism of the flip graph of a surface without boundary is ind…

It is shown that timelike surfaces of constant mean curvature 1 in anti-de Sitter 3-space can be constructed from a pair of Lorentz holomorphic and Lorentz antiholomorphic null curves in PSL(2,R) via Bryant type representation formulae. These formulae are used to investigate an explicit one-to-one correspondence, the s…

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