论文标题
亚里曼尼亚次棕色运动和应用的径向过程
Radial processes for sub-Riemannian Brownian motions and applications
论文作者
论文摘要
我们研究了完全大地叶的背景下，研究了伊曼尼亚人布朗运动的径向部分。事实证明，ITô的公式用于与涉及riemannian的Riemannian距离相关的径向过程。我们推断出非常通用的随机完整性标准，以供伊曼尼亚人布朗尼运动。在Sasakian叶子和H型组的背景下，人们可以进一步推动分析，并利用最近证明的亚拉平质比较定理，可以比较亚军距离的径向过程与一维模型扩散。作为一种几何应用，我们证明了Cheng的类型估计值对亚riemannian公制球的差异特征值的估计，即使在海森伯格组中，这似乎是新的。
We study the radial part of sub-Riemannian Brownian motion in the context of totally geodesic foliations. Itô's formula is proved for the radial processes associated to Riemannian distances approximating the Riemannian one. We deduce very general stochastic completeness criteria for the sub-Riemannian Brownian motion. In the context of Sasakian foliations and H-type groups, one can push the analysis further, and taking advantage of the recently proved sub-Laplacian comparison theorems one can compare the radial processes for the sub-Riemannian distance to one-dimensional model diffusions. As a geometric application, we prove Cheng's type estimates for the Dirichlet eigenvalues of the sub-Riemannian metric balls, a result which seems to be new even in the Heisenberg group.
