A note on harmonic maps between surfaces

On Quasiconformal Harmonic Maps between Surfaces

It is proved the following theorem, if w is a quasiconformal harmonic mappings between two Riemann surfaces with smooth boundary and aproximate analytic metric, then w is a quasi-isometry with respect to Euclidean metric.

Reversible Harmonic Maps between Discrete Surfaces

Information transfer between triangle meshes is of great importance in computer graphics and geometry processing. To facilitate this process, a smooth and accurate map is typically required between the two meshes. While such maps can sometimes be computed between nearly-isometric meshes, the more general case of meshes with diverse geometries remains challenging. We propose a novel approach for...

Stable Exponentially Harmonic Maps Between Finsler Manifolds

stable exponentially harmonic maps between finsler manifolds

Measured Foliations and Harmonic Maps of Surfaces

Fix a Riemannian surface of negative curvature (N, h), and a differentiable surface M g of the same genus g that will host various structures. Also fix a diffeomorphism f0 : M → N . It is well known ([ES], [A], [SY1], [Sa]) that to every complex structure σ on M , there is a unique harmonic diffeomorphism f(σ) : M(σ) → (N, h) homotopic to f0 : M → N ; one is led to consider what other, possibly...