Construction of harmonic diffeomorphisms and minimal graphs
微分几何
2007-05-23 v1
摘要
We study complete minimal graphs in HxR, which take asymptotic boundary values plus and minus infinity on alternating sides of an ideal inscribed polygon Γ in H. We give necessary and sufficient conditions on the "lenghts" of the sides of the polygon (and all inscribed polygons in Γ) that ensure the existence of such a graph. We then apply this to construct entire minimal graphs in HxR that are conformally the complex plane C. The vertical projection of such a graph yields a harmonic diffeomorphism from C onto H, disproving a conjecture of Rick Schoen.
引用
@article{arxiv.math/0701547,
title = {Construction of harmonic diffeomorphisms and minimal graphs},
author = {Pascal Collin and Harold Rosenberg},
journal= {arXiv preprint arXiv:math/0701547},
year = {2007}
}