Pansu pullback and exterior differentiation for Sobolev maps on Carnot groups
| Autor: | Kleiner, Bruce, Muller, Stefan, Xie, Xiangdong |
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| Rok vydání: | 2020 |
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| Druh dokumentu: | Working Paper |
| Popis: | We show that in an $m$-step Carnot group, a probability measure with finite $m^{th}$ moment has a well-defined Buser-Karcher center-of-mass, which is a polynomial in the moments of the measure, with respect to exponential coordinates. Using this, we improve the main technical result of our previous paper concerning Sobolev mappings between Carnot groups; as a consequence, a number of rigidity and structural results from recent papers hold under weaker assumptions on the Sobolev exponent. We also give applications to quasiregular mappings, extending earlier work in the $2$-step case to general Carnot groups. Comment: This version includes new sections covering product rigidity and mappings between complexified Carnot groups, as well as a number of small corrections and changes |
| Databáze: | arXiv |
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