https://neckpinch.com/authors/batu-guneysu/New arXiv papers by Batu Güneysu, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/2003.10204/arxiv:2003.10204Mon, 23 Mar 2020 00:00:00 GMTSebastian Boldt, Batu Güneysu — Given a noncompact spin manifold M with a fixed topological spin structure and two complete Riemannian metrics g and h on M with bounded sectional curvatures, we prove a criterion for the existence and completeness of the wave operators 𝓦_(±)(Dₕ, D_g, I_(g,h)) and 𝓦_(±)(Dₕ², D²_g, I_(g,h)), where I_(g,h) is the canonically given unitary map between the underlying L²-spaces of spinors. This criterion does not involve any injectivity radius assumptions and leads to a criterion for the stability of the absolutely continuous spectrum of a Dirac operator and its square under a Ricci flow.Ricci flowStability & uniquenessBoundaries & non-compactEigenvalues & spectrum https://neckpinch.com/papers/1709.01612/arxiv:1709.01612Tue, 05 Sep 2017 00:00:00 GMTBatu Güneysu, Anton Thalmaier — We prove a completely new integral criterion for the existence and completeness of the wave operators W_(±)(−Δₕ,−Δ_g, I_(g,h)) corresponding to the (unique self-adjoint realizations of) the Laplace-Beltrami operators −Δⱼ, j=1,2, that are induced by two quasi-isometric complete Riemannian metrics g and h on an open manifold M. In particular, this result provides a criterion for the absolutely continuous spectra of −Δ_g and −Δₕ to coincide. Our proof relies on estimates that are obtained using a probabilistic Bismut type formula for the gradient of a heat semigroup. Unlike all previous results, our integral criterion only requires some lower control on the Ricci curvatures and some upper control on the heat kernels, but no control at all on the injectivity radii. As a consequence, we obtain a stability result for the absolutely continuous spectrum under a Ricci flow.Ricci flowGeneralized & G₂ flowsHeat kernelStability & uniquenessEigenvalues & spectrum