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

这个项目的中心主题是这样一个问题：黎曼流形上的拉普拉斯和热流在恒定的Ricci曲率下界下的经典性质将在多大程度上扩展到加权黎曼流形的情况，其中Bakry-Emery-Ricci张量仅由Kato类函数从下有界。这样的加权流形看起来很自然，例如通过量子力学中的基态变换。我们希望使用分析、几何和概率论技术的广泛组合。

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.