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arXiv · 2007.06694

Pansu pullback and exterior differentiation for Sobolev maps on Carnot groups

Bruce Kleiner·Stefan Muller·Xiangdong Xie
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Abstract

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.

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Bruce Kleiner, Stefan Muller, Xiangdong Xie. 2020-07-13. Pansu pullback and exterior differentiation for Sobolev maps on Carnot groups. https://arxiv.org/abs/2007.06694

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