论文标题
亚riemannian几何形状中亚曼叶的相对热含量
The relative heat content for submanifolds in sub-Riemannian geometry
论文作者
论文摘要
我们研究亚riemannian几何形状中亚曼叶的相对热含量的小渐近物。首先，假设它们没有特征点，我们证明了对任何编码的子延伸的平滑管状邻域的存在。接下来，我们提出一个针对Codimension $ k \ geq 1 $的子手机的相对热含量的定义，并通过光滑的管状社区建立了此数量的近似值。最后，我们表明，这种近似未能通过研究明确的例子来恢复亚体的相对热含量的渐近扩张。
We study the small-time asymptotics of the relative heat content for submanifolds in sub-Riemannian geometry. First, we prove the existence of a smooth tubular neighborhood for submanifolds of any codimension, assuming they do not have characteristic points. Next, we propose a definition of relative heat content for submanifolds of codimension $k\geq 1$ and we build an approximation of this quantity, via smooth tubular neighborhoods. Finally, we show that this approximation fails to recover the asymptotic expansion of the relative heat content of the submanifold, by studying an explicit example.
