Dr. Christian Rose

Publications in peer-reviewed journals

• C. Rose. Off-diagonal upper heat kernel bounds on graphs with unbounded geometry. To appear in Indagationes Mathematicae. arXiv
   
• F. Fischer and C. Rose. Optimal Poincaré-Hardy-type Inequalities on Manifolds and Graphs. To appear in Indagationes Mathematicae. 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
• 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

Contributions to books

• 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.

Theses

• 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.

Submitted articles 

• P. Bifulco, J. Kerner and C. Rose. Spectral comparison results for Laplacians on discrete graphs. 2024. arXiv
   
• C. Rose. Gaussian upper heat kernel bounds and Faber-Krahn inequalities on graphs. 2024. arXiv
   
• 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

WS 25/26 University of Potsdam

Vorlesung "Analysis III". Tragen Sie sich bitte bei Moodle und PULS ein. 

Lecture "Partial Differential Equations I". Please subscribe to Moodle and PULS. 

SS 24 University of Potsdam

Vorlesung "Mathematik für Physiker_innen II" (bis 30.4.2024). Tragen Sie sich bitte bei Moodle und PULS ein.

WS 23/24 University of Potsdam

Vorlesung "Mathematik für Physiker_innen I". Tragen Sie sich bitte bei Moodle und PULS ein. 

Seminar "Analysis and heat kernels on graphs". Please subscribe to Moodle and PULS. 

WS 21/22 University of Bremen

Lecture "Funktionentheorie".

Seminar "Einführung in die Analysis auf Graphen".

SS 21 University of Potsdam

Lecture "Topologie". Moodle