Dr. rer. nat. Christian Rose

I work on various topics in geometric and global analysis on manifolds and graphs, e.g., spectral and geometric implications of Ricci curvature bounds, general properties of solutions to the heat equation, and related topics. Besides this, I also became interested in non-linear problems such as harmonic heat or mean curvature flow.

• X. Ramos Olivé, C. Rose, L. Wang, and G. Wei: Integral Ricci curvature and the mass gap of Dirichlet Laplacians on domains. 2020. arXiv
• A. Dicke, C. Rose, A. Seelmann, and M. Tautenhahn. Quantitative unique continuation for spectral subspaces of Schrödinger operators with singular potentials. 2020. arXiv
• O. Post, X. Ramos, and C. Rose. Quantitative Sobolev extensions and the Neumann heat kernel under integral Ricci curvature conditions. 2020. arXiv
• J. Jost, F. Münch, and C. Rose. Liouville property and non-negative Ollivier curvature on graphs. 2019. arXiv
• M. Hansmann, C. Rose, and P. Stollmann. Bounds on the first Betti number - an approach via Schatten norm estimates on semigroup differences. 2018. arXiv

• C. Rose. Almost positive Ricci curvature in Kato sense - an extension of Myers' theorem. To appear in Mathematical Research Letters. arXiv
• C. Rose and G. Wei. Eigenvalue estimates under Kato-type Ricci curvature conditions. To appear in Analysis & PDE. arXiv
• G. Carron and C. Rose. Geometric and spectral estimates based on spectral Ricci curvature assumptions. Journal für die Reine und Angewandte Mathematik. 2020. online first, doi:10.1515/crelle-2020-0026 arXiv
• F. Münch and C. Rose. Spectrally positive Bakry-Émery Ricci curvature on graphs. Journal de Mathématiques Pures et Appliquées, 143: 334--344, 2020. arXiv
• S. Liu, F. Münch, N. Peyerimhoff, and C. Rose. Distance bounds for graphs with some negative Bakry-Émery Ricci curvature. Analysis and Geometry on Metric Spaces, 7(1):1--14, 2019. arXiv
• C. Rose. Li-Yau gradient estimate for compact manifolds with negative part of Ricci curvature in the Kato class. Annals of Global Analysis and Geometry, 55(3):443--449,2019. arXiv
• I. Nakić, C. Rose, and M. Tautenhahn. A quantitative Carleman estimate for second order elliptic operators. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 149(4): 915--938, 2019. arXiv
• C. Rose. Heat kernel upper bound on Riemannian manifolds with locally uniform Ricci curvature integral bounds. Journal of Geometric Analysis, 27:1737--1750, 2017. arXiv
• C. Rose and P. Stollmann. The Kato class on compact manifolds with integral bounds on the negative part of Ricci curvature. Proceedings of the American Mathematical Society, 145(5): 2199--2210, 2017. arXiv

• C. Rose and P. Stollmann. Manifolds with Ricci curvature in the Kato class: heat kernel bounds and applications. In Analysis and Geometry on Graphs and Manifolds, Volume 461 of London Mathematical Society Lecture Note Series, Cambridge University Press, 2020.
• D. Borisov, I. Nakić, C. Rose, M. Tautenhahn, and I. Veselić. Multiscale unique continuation properties of eigenfunctions. In Operator semigroups meet complex analysis, harmonic analysis and mathematical physics, volume 250 of Operator Theory Adv. Appl., pages 107--118. Birkhäuser/Springer, Cham., 2015.

• Heat kernel estimates based on Ricci curvature integral bounds. PhD thesis, 2017. Advisor: Prof. Dr. Peter Stollmann, Technische Universität Chemnitz.
• Über die Wärmeleitungshalbgruppe auf Mannigfaltigkeiten. Diploma thesis, 2014. Advisor: Prof. Dr. Peter Stollmann, Technische Universität Chemnitz.