论文标题
在海森堡组中退化特征点下二曼尼亚平均曲率的一致性
Integrability of the sub-Riemannian mean curvature at degenerate characteristic points in the Heisenberg group
论文作者
论文摘要
我们解决了围绕孤立的特征点嵌入的超表面的亚riemannian平均曲率的整合性问题。本说明的主要贡献是引入了海森堡组平滑表面的轻度退化特征点的概念，在一个邻域中，伊曼尼亚的平均值曲率是可以集成的（相对于由欧几里得结构引起的周边度量）。结果，我们部分回答了Danielli-Garofalo-Nhieu在[Danielli D.，Garofalo N.，Nhieu D.M.，Proc。阿米尔。数学。 Soc。，2012]，证明具有离散特征集的实验表面的平均曲率是可以局部整合的。
We address the problem of integrability of the sub-Riemannian mean curvature of an embedded hypersurface around isolated characteristic points. The main contribution of this note is the introduction of a concept of mildly degenerate characteristic point for a smooth surface of the Heisenberg group, in a neighborhood of which the sub-Riemannian mean curvature is integrable (with respect to the perimeter measure induced by the Euclidean structure). As a consequence we partially answer to a question posed by Danielli-Garofalo-Nhieu in [Danielli D., Garofalo N., Nhieu D.M., Proc. Amer. Math. Soc., 2012], proving that the mean curvature of a real-analytic surface with discrete characteristic set is locally integrable.
