Probabilistic and Spectral Properties of Weighted Riemannian Manifolds with Kato-bounded Bakry-Emery-Ricci Curvature

具有 Kato 有界 Bakry-Emery-Ricci 曲率的加权黎曼流形的概率和谱特性

• 批准号: 442045221
• 负责人: Professor Dr. Batu Güneysu
• 金额: --
• 依托单位: Mathematisches Institut
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/442045221?language=en
• 关键词: Probabilistic; Spectral; Properties; Weighted; Riemannian

The central theme of the project ist the question to what extent classical properties of the Laplacian and the heat flow on a Riemannian manifold under constant lower Ricci curvature bound will extend to the case of weighted Riemannian manifolds where nor the Bakry-Emery-Ricci tensor is bounded from below only by a Kato class function. Such weighted manifolds appear naturally e.g. through ground state transformation in quantum mechanics. We expect to use a wide combination of analytic, geometric and probablistic technques.

该项目的中心主题是这样一个问题，在什么程度上的经典性质的拉普拉斯算子和热流的黎曼流形下常数较低的里奇曲率界将延伸到加权黎曼流形的情况下，也没有Bakry-Emery-Ricci张量是有界的从下面只有一个加藤类函数。这样的加权流形自然出现，例如通过量子力学中的基态变换。我们希望使用分析，几何和概率技术的广泛结合。