Dr. Christian Rose

My general research interests are

• Differential geometry,
• Global analysis, analysis on manifolds and (discrete) graphs,
• Partial differential equations, 

as well as the interplay between these areas. Currently, I am the principal investigator of the project "Heat kernel behavior at infinity on graphs" funded by the DFG.

• C. Rose. Gaussian upper heat kernel bounds and Faber-Krahn inequalities on graphs. 2024. 
   
• M. Keller and C. Rose. Gaussian upper bounds, volume doubling and Sobolev inequalities on graphs. 2024. arXiv
   
• M. Keller and C. Rose. Gaussian upper bounds for heat kernels on graphs with unbounded geometry. 2022. arXiv
  ​​​​​​​
• J. Jost, F. Münch, and C. Rose. Liouville property and non-negative Ollivier curvature on graphs. 2019. arXiv

• C. Rose and M. Tautenhahn. Unique continuation estimates on manifolds with Ricci curvature bounded below. Journal of Mathematical Physics, 65 (4): Article number 041503, 2024. Journal arXiv
   
• M. Keller and C. Rose. Anchored heat kernel upper bounds on graphs with unbounded geometry and anti-trees. Calculus of Variations and Partial Differential Equations, 63, Article number: 20, 2024. Journal arXiv
   
• A. Dicke, C. Rose, A. Seelmann, and M. Tautenhahn. Quantitative unique continuation for spectral subspaces of Schrödinger operators with singular potentials. Journal of Differential Equations, 369: 405-–423, 2023. Journal arXiv
   
• X. Ramos Olivé, C. Rose, L. Wang, and G. Wei. Integral Ricci curvature and the mass gap of Dirichlet Laplacians on domains. Mathematische Nachrichten, 296 (8):  3559--3578. 2023. Journal arXiv
   
• O. Post, X. Ramos Olivé, and C. Rose. Quantitative Sobolev extensions and the Neumann heat kernel for integral Ricci curvature conditions. Journal of Geometric Analysis, 33: 70, 2023. Journal arXiv
   
• C. Rose and G. Wei. Eigenvalue estimates under Kato-type Ricci curvature conditions.  Analysis & PDE, 15(7): 1703--1724, 2022. Journal arXiv
   
• M. Hansmann, C. Rose, and P. Stollmann. Bounds on the first Betti number - an approach via Schatten norm estimates on semigroup differences. Journal of Geometric Analysis, 32(4): 1--17, 2022. Journal arXiv
   
• C. Rose. Almost positive Ricci curvature in Kato sense - an extension of Myers' theorem. Mathematical Research Letters, 28(6): 1841--1849, 2021. Journal arXiv
   
• G. Carron and C. Rose. Geometric and spectral estimates based on spectral Ricci curvature assumptions. Journal für die Reine und Angewandte Mathematik. 2021 (772): 121--145, 2021. Journal arXiv
   
• F. Münch and C. Rose. Spectrally positive Bakry-Émery Ricci curvature on graphs. Journal de Mathématiques Pures et Appliquées, 143: 334--344, 2020. Journal 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.
   
• 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. Journal 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. Journal 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. Journal 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. Journal 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. Journal arXiv
   
• 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.