Quasiregular mappings between equiregular SubRiemannian manifolds
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2015
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| _version_ | 1866913460686684160 |
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| author | Guo, Chang-Yu Golo, Sebastiano Nicolussi Williams, Marshall Xuan, Yi |
| author_facet | Guo, Chang-Yu Golo, Sebastiano Nicolussi Williams, Marshall Xuan, Yi |
| contents | In this paper, we provide an alternative appraoch to an expectaion of Fässler 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1505_00891 |
| institution | arXiv |
| publishDate | 2015 |
| record_format | arxiv |
| spellingShingle | Quasiregular mappings between equiregular SubRiemannian manifolds Guo, Chang-Yu Golo, Sebastiano Nicolussi Williams, Marshall Xuan, Yi Complex Variables 53C17, 30C65, 58C06 In this paper, we provide an alternative appraoch to an expectaion of Fässler 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. |
| title | Quasiregular mappings between equiregular SubRiemannian manifolds |
| topic | Complex Variables 53C17, 30C65, 58C06 |
| url | https://arxiv.org/abs/1505.00891 |