Reversible Harmonic Maps between Discrete Surfaces

Numerical analysis of a finite element scheme for the approximation of harmonic maps into surfaces

This article studies the numerical approximation of harmonic maps into surfaces, i.e., critical points for the Dirichlet energy among weakly differentiable vector fields that are constrained to attain their pointwise values in a given manifold. An iterative algorithm that is based on a linearization of the constraint about the current iterate at the nodes of a triangulation is devised and its g...

Harmonic Morphisms and Hyperelliptic Graphs

We study harmonic morphisms of graphs as a natural discrete analogue of holomorphic maps between Riemann surfaces. We formulate a graph-theoretic analogue of the classical RiemannHurwitz formula, study the functorial maps on Jacobians and harmonic 1-forms induced by a harmonic morphism, and present a discrete analogue of the canonical map from a Riemann surface to projective space. We also disc...

Stable Exponentially Harmonic Maps Between Finsler Manifolds

High Quality Surface Remeshing Using Harmonic Maps

In this paper, we present an efficient and robust technique for surface remeshing based on harmonic maps. We show how to ensure a one-to-one mapping for the discrete harmonic map and introduce a cubic representation of the geometry based on curved PN triangles. Topological and geometrical limitations of harmonic maps are also put to the fore and discussed. We show that, with the proposed approa...

Minimal Graphs in H × R and Their Projections

June 29, 2007 There has been a recent resurgence of interest in the subject of minimal surfaces in product three-manifolds, for example H ×R [Ros02], [MR04], [MIR05], [NR02], [Dan06], [FM05], [HET05]. The purpose of this note is to describe a construction and some examples originating in the harmonic maps literature whose consequences for minimal surfaces seem to have escaped notice. We organiz...