论文标题
在接触式亚riemannian歧管中进行超曲面的固有亚拉普拉斯
Intrinsic sub-Laplacian for hypersurface in a contact sub-Riemannian manifold
论文作者
论文摘要
我们构建和研究了在特征点之外定义的内在亚拉普拉斯式，以使嵌入在接触式亚riemannian歧管中的平滑性超表面。我们证明，远离特征点，固有的次拉普拉斯人是通过使用Reeb vector Field构建的riemannian近似近似值的Laplace-Beltrami操作员的极限。我们仔细分析了三个模型案例的家族，用于通过考虑嵌入在模型空间中的典型空间中的典型超曲面，以获得接触式亚riemannian歧管。在这些模型案例中，我们表明内在的亚拉普拉斯人随机完整，尤其是，固有的亚拉普拉斯式诱导的随机过程几乎肯定不会达到特征点。
We construct and study the intrinsic sub-Laplacian, defined outside the set of characteristic points, for a smooth hypersurface embedded in a contact sub-Riemannian manifold. We prove that, away from characteristic points, the intrinsic sub-Laplacian arises as the limit of Laplace-Beltrami operators built by means of Riemannian approximations to the sub-Riemannian structure using the Reeb vector field. We carefully analyse three families of model cases for this setting obtained by considering canonical hypersurfaces embedded in model spaces for contact sub-Riemannian manifolds. In these model cases, we show that the intrinsic sub-Laplacian is stochastically complete and in particular, that the stochastic process induced by the intrinsic sub-Laplacian almost surely does not hit characteristic points.
