接触子黎曼流形中超曲面的内禀子拉普拉斯

IF 1.1 4区 数学 Q2 MATHEMATICS, APPLIED
Davide Barilari, Karen Habermann
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引用次数: 1

摘要

构造并研究了嵌入在接触子黎曼流形中的光滑超曲面的特征点集外的内禀子拉普拉斯算子。我们证明了在远离特征点的地方,内禀子拉普拉斯算子是利用Reeb向量场对子黎曼结构进行黎曼逼近所建立的拉普拉斯-贝尔特拉米算子的极限。我们仔细分析了通过考虑嵌入在接触亚黎曼流形模型空间中的正则超曲面而得到的这种设置的三种模型情况。在这些模型情况下,我们证明了内禀子拉普拉斯算子是随机完备的,特别是,由内禀子拉普拉斯算子引起的随机过程几乎肯定不会击中特征点。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Intrinsic sub-Laplacian for hypersurface in a contact sub-Riemannian manifold
Abstract 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.
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来源期刊
CiteScore
1.70
自引率
8.30%
发文量
75
审稿时长
>12 weeks
期刊介绍: Nonlinear Differential Equations and Applications (NoDEA) provides a forum for research contributions on nonlinear differential equations motivated by application to applied sciences. The research areas of interest for NoDEA include, but are not limited to: deterministic and stochastic ordinary and partial differential equations, finite and infinite-dimensional dynamical systems, qualitative analysis of solutions, variational, topological and viscosity methods, mathematical control theory, complex dynamics and pattern formation, approximation and numerical aspects.
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