论文标题
Carnot组中均匀可区分的共同体固有图的表征
Characterizations of uniformly differentiable co-horizontal intrinsic graphs in Carnot groups
论文作者
论文摘要
在任意的Carnot组中，我们研究具有水平靶标的图的固有图。这些图是$ c^1_h $正常定期的，当地图均匀地本质上可区分时。我们的第一个主要结果是沿图上左右不变矢量场的投影的Hölder属性来表征均匀的内在可区分性。我们通过仅需要水平规律性来加强步骤2 Carnot组的固有实价图。我们指出，在最简单的Step-3组中，这种完善是不可能的。作为独立利益的副产品，在每个Carnot群体中，我们都证明了一个面积均匀固有可区分的实值图的面积。我们还根据地图的固有导数明确地编写了区域元素。
In arbitrary Carnot groups we study intrinsic graphs of maps with horizontal target. These graphs are $C^1_H$ regular exactly when the map is uniformly intrinsically differentiable. Our first main result characterizes the uniformly intrinsic differentiability by means of Hölder properties along the projections of left-invariant vector fields on the graph. We strengthen the result in step-2 Carnot groups for intrinsic real-valued maps by only requiring horizontal regularity. We remark that such a refinement is not possible already in the easiest step-3 group. As a by-product of independent interest, in every Carnot group we prove an area-formula for uniformly intrinsically differentiable real-valued maps. We also explicitly write the area element in terms of the intrinsic derivatives of the map.
