Closure of the Laplace-Beltrami Operator on 2D Almost-Riemannian Manifolds and Semi-Fredholm Properties of Differential Operators on Lie Manifolds

被引：0
作者：
Ivan Beschastnyi
机构：
[1] University of Aveiro,Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics
来源：
Results in Mathematics | 2023年 / 78卷
关键词：
Almost-Riemannian geometry; Laplace-Beltrami operator; Lie groupoids; Semi-Fredholm conditions; 58J05; 58J60; 47A53; 47F10;
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学科分类号：
摘要：
The problem of determining the domain of the closure of the Laplace-Beltrami operator on a 2D almost-Riemannian manifold is considered. Using tools from theory of Lie groupoids natural domains of perturbations of the Laplace-Beltrami operator are found. The main novelty is that the presented method allows us to treat geometries with tangency points. This kind of singularity is difficult to treat since those points do not have a tubular neighbourhood compatible with the almost-Riemannian metric.
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