Dr. habil. Batu Güneysu

Prof. Dr. Batu Güneysu

Project leader

Christian-Albrechts-Universität zu Kiel

zbMATH profile: https://zbmath.org/authors/?q=au%3A%22Ba…

Project

50Probabilistic and spectral properties of weighted Riemannian manifolds with Kato bounded Bakry-Emery-Ricci curvature

Publications within SPP2026

Batu Güneysu, M. Marot: A note on the scattering theory of Kato-Ricci manifolds (2024)

We prove a new criterion for the existence and completeness of the wave operators corresponding to the Laplace-Beltrami operators corresponding to two Riemannian metrics on a fixed noncompact manifold. Our result relies on recent estimates on the heat semigroup and its derivative, that are valid if the negative part of the Ricci curvature is in the Kato class - so called Kato-Ricci manifolds.

Journal	Rocky Mountain Journal of Mathematics
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Sebastian Boldt, Batu Güneysu: Feynman-Kac formula for perturbations of order ≤1, and noncommutative geometry. (2023)

We prove a Feynman-Kac formula for the (nonselfadjoint) semigroups whose generators are first order perturbations of Laplacians on vector bundles over noncompact Riemannian manifolds. Applications to noncommutative geometry (linked to the geometry of loop spaces) are presented.

Journal	Stochastics and Partial Differential Equations: Analysis and Computations
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Batu Güneysu, Kazuhiro Kuwae: Locally convex aspects of the Kato and the Dynkin classes on manifolds (2023)

We show that the local Kato class on a smooth Riemannian manifold, defined in terms of the underlying heat kernel, does not depend on the underlying Riemannian metric, and thus becomes a well-defined Frechet space on any smooth manifold.

Journal	Illinois J. Math.
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Batu Güneysu: RCD(K,N) spaces and the geometry of multi-particle Schrödinger semigroups (2022)

Given an RCD space with Cheeger Laplacian H, we introduce the corresponding α-Kato class of potentials, and we show that the semigroups associated with H+V, where V is α-Kato, is α-Hölder-smoothing.

Journal	International Mathematics Research Notices
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Batu Güneysu, Max von Renesse: Molecules as metric measure spaces with Kato-bounded Ricci curvature (2021)

We show that the metric measure space given by Euclidean space together with the Lebesgue measure weighted by the ground state of an electron has a Bakry-Emery-Ricci tensor which is bounded by a Kato function. We also show that the corresponding diffusion is stochastically complete.

Journal	C. R. Math. Acad. Sci. Paris
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