Harmonic maps between 3-dimensional hyperbolic spaces

• 成果类型: Article
• 署名作者: Markovic, Vladimir
• 署名单位: California Institute of Technology
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-014-0536-x
• 发表日期: 2015
• 页码: 921-951
• 关键词: dirichlet problem; uniqueness; MANIFOLDS; REGULARITY; extension; CURVATURE; INFINITY; mappings

摘要

We prove that a quasiconformal map of the sphere S-2 admits a harmonic quasi-isometric extension to the hyperbolic space H-3, thus confirming the well known Schoen Conjecture in dimension 3.