Quasiregular mappings between equiregular SubRiemannian manifolds
| Autor: | Guo, Chang-Yu, Golo, Sebastiano Nicolussi, Williams, Marshall, Xuan, Yi |
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| Rok vydání: | 2015 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In this paper, we provide an alternative appraoch to an expectaion of F\"assler et al [J. Geom. Anal. 2016] by showing that a metrically quasiregular mapping between two equiregular subRiemannian manifolds of homogeneous dimension $Q\geq 2$ has a negligible branch set. One main new ingredient is to develop a suitable extension of the generalized Pansu differentiability theory, in spirit of earlier works by Margulis-Mostow, Karmanova and Vodopyanov. Another new ingredient is to apply the theory of Sobolev spaces based on upper gradients developed by Heinonen, Koskela, Shanmugalingam and Tyson to establish the necessary analytic foundations. Comment: 50 pages, major changes based on comments from experts |
| Databáze: | arXiv |
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