On Quasi-conformal 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...

Conformal Maps and Minimal Surfaces

Stable Exponentially Harmonic Maps Between Finsler Manifolds

Conformal and Harmonic Measures on Laminations Associated with Rational Maps

The framework of aane and hyperbolic laminations provides a unifying foundation for many aspects of conformal dynamics and hyperbolic geometry. The central objects of this approach are an aane Riemann surface lamination A and the associated hyperbolic 3-lamination H endowed with an action of a discrete group of iso-morphisms. This action is properly discontinuous on H, which allows one to pass ...