论文标题
pansu的回调和sobolev maps的外部分化
Pansu pullback and exterior differentiation for Sobolev maps on Carnot groups
论文作者
论文摘要
我们表明，在一个$ m $步骤Carnot组中，具有有限$ M^{th} $时刻的概率度量有一个定义明确的Buser-Karcher质量中心，这是该度量时刻的多项式，就指数坐标而言。使用它，我们改善了以前关于Carnot组之间Sobolev映射的论文的主要技术结果；结果，最近论文的许多刚性和结构性结果在Sobolev指数的较弱的假设下。我们还向Quasiregular映射提供了申请，将$ 2 $步骤的案例的早期工作扩展到了普通Carnot组。
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.
