https://neckpinch.com/authors/oliver-lindblad-petersen/New arXiv papers by Oliver Lindblad Petersen, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/2009.11854/arxiv:2009.11854Thu, 24 Sep 2020 00:00:00 GMTKlaus Kroencke, Oliver Lindblad Petersen — We prove stability of integrable ALE manifolds with a parallel spinor under Ricci flow, given an initial metric which is close in L^p ∩ L^∞, for any p ∈ (1, n), where n is the dimension of the manifold. In particular, our result applies to all known examples of 4-dimensional gravitational instantons. Our decay rates are strong enough to prove positive scalar curvature rigidity in L^p, for each p ∈ [1, n/(n-2)), generalizing a result by Appleton.Ricci flowRicci-flat & Calabi–YauScalar curvatureStability & uniqueness https://neckpinch.com/papers/2006.06662/arxiv:2006.06662Thu, 11 Jun 2020 00:00:00 GMTKlaus Kroencke, Oliver Lindblad Petersen — We consider the heat equation associated to Schrödinger operators acting on vector bundles on asymptotically locally Euclidean (ALE) manifolds. Novel L^p − L^q decay estimates are established, allowing the Schrödinger operator to have a non-trivial L²-kernel. We also prove new decay estimates for spatial derivatives of arbitrary order, in a general geometric setting. Our main motivation is the application to stability of non-linear geometric equations, primarily Ricci flow, which will be presented in a companion paper. The arguments in this paper use that many geometric Schrödinger operators can be written as the square of Dirac type operators. By a remarkable result of Wang, this is even true for the Lichnerowicz Laplacian, under the assumption of a parallel spinor. Our analysis is based on a novel combination of the Fredholm theory for Dirac type operators on ALE manifolds and recent advances in the study of the heat kernel on non-compact manifolds.Ricci flowRicci-flat & Calabi–YauHeat kernelStability & uniquenessBoundaries & non-compact https://neckpinch.com/papers/1903.03502/arxiv:1903.03502Fri, 08 Mar 2019 00:00:00 GMTKlaus Kroencke, Oliver Lindblad Petersen, Felix Lubbe, Tobias Marxen, Wolfgang Maurer, Wolfgang Meiser, Oliver C. Schnürer, Áron Szabó, Boris Vertman — We consider the long-time behaviour of the mean curvature flow of spacelike hypersurfaces in the Lorentzian product manifold M×ℝ, where M is asymptotically flat. If the initial hypersurface F₀⊂ M×ℝ is uniformly spacelike and asymptotic to M×s\ for some s∈ℝ at infinity, we show that a mean curvature flow starting at F₀ exists for all times and converges uniformly to M×s\ as t→ ∞.Mean curvature flowBoundaries & non-compactLong-time existence & convergencePhysics