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

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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.