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Applications of Quaternionic Holomorphic Geometry to minimal surfaces

K. Leschke, K. Moriya (2016)

Complex Manifolds

In this paper we give a survey of methods of Quaternionic Holomorphic Geometry and of applications of the theory to minimal surfaces. We discuss recent developments in minimal surface theory using integrable systems. In particular, we give the Lopez–Ros deformation and the simple factor dressing in terms of the Gauss map and the Hopf differential of the minimal surface. We illustrate the results for well–known examples of minimal surfaces, namely the Riemann minimal surfaces and the Costa surface....

Approximate roots of pseudo-Anosov diffeomorphisms

T. M. Gendron (2009)

Annales de l’institut Fourier

The Root Conjecture predicts that every pseudo-Anosov diffeomorphism of a closed surface has Teichmüller approximate $n$ th roots for all $n \geq 2$ . In this paper, we replace the Teichmüller topology by the heights-widths topology – that is induced by convergence of tangent quadratic differentials with respect to both the heights and widths functionals – and show that every pseudo-Anosov diffeomorphism of a closed surface has heights-widths approximate $n$ th roots for all $n \geq 2$ .

We give an upper bound for the order of an automorphism of a Riemann surface with two fixed points. The main results are presented in Theorems 1.4 and 2.4.

Displaying 81 – 92 of 92

Applications of Quaternionic Holomorphic Geometry to minimal surfaces

Approximate roots of pseudo-Anosov diffeomorphisms

Approximation auf abgeschlossenen Teilen Riemannscher Flächen.

Approximation of a map between one-dimensional Teichmüller spaces.

Arithmetic Fuchsian groups and the number of systoles.

Associated Curves and Plücker Formulas in Grassmannians.

Automorphism groups of compact Klein surfaces with one boundary component.

Automorphism Groups of Compact Planar Klein Surfaces.

Automorphism groups of orientable elliptic-hyperelliptic Klein surfaces.

Automorphism groups of Schottky type.

Automorphismen und Modularraum Galoisscher dreiblättriger Überlagerungen.

Automorphisms of Riemann surfaces with two fixed points

Currently displaying 81 – 92 of 92