Dr. rer. nat. Christian Rose

Postdoktorand

Kontakt
Raum:
2.09.3.13
Telefon:
+49 331 977-203153

Teaching

Seminar "Einführung in die Analysis auf Graphen" WS 21/22 University of Bremen

Lecture "Funktionentheorie" WS 21/22 University of Bremen

Lecture "Topologie" SS 21 University of Potsdam, see Moodle

Research Interests

I work on various topics in geometric and global analysis on manifolds and graphs. This includes spectral and geometric implications of Ricci curvature bounds, properties of solutions of heat and Laplace-type equations, and related topics.

Submitted preprints

  • M. Keller and C. Rose. Gaussian upper bounds for heat kernels on graphs with unbounded geometry. 2022. arXiv
  • X. Ramos Olivé, C. Rose, L. Wang, and G. Wei. Integral Ricci curvature and the mass gap of Dirichlet Laplacians on domains. 2021. arXiv
  • A. Dicke, C. Rose, A. Seelmann, and M. Tautenhahn. Quantitative unique continuation for spectral subspaces of Schrödinger operators with singular potentials. 2020. arXiv
  • J. Jost, F. Münch, and C. Rose. Liouville property and non-negative Ollivier curvature on graphs. 2019. arXiv

Articles in peer-reviewed journals

  • O. Post, X. Ramos, and C. Rose. Quantitative Sobolev extensions and the Neumann heat kernel for integral Ricci curvature conditions. To appear in Journal of Geometric Analysis. arXiv
  • C. Rose and G. Wei. Eigenvalue estimates under Kato-type Ricci curvature conditions. To appear in Analysis & PDE. 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.

CV

04/2022 - todayPostdoc, Universität Potsdam
10/2021 - 03/2022  Deputy professor, Universität Bremen
12/2020 - 09/2021 Postdoc, Universität Potsdam
10/2018 - 09/2020 Postdoc, Max Planck Institute for Mathematics in the Sciences, Leipzig
09/2017 - 09/2018 Postdoc, Technische Universität Chemnitz
06/2014 - 08/2017 PhD student, Technische Universität Chemnitz
10/2009 - 05/2014 Undergrad Studies in Mathematics, Technische Universität Chemnitz