Dr. rer. nat. Christian Rose

Postdoktorand

Kontakt
Raum:
2.09.3.13
Telefon:
+49 331 977-1551

Research Interests

  • global and geometric analysis on manifolds and graphs
  • spectral theory of Schrödinger operators 

Submitted preprints

  • 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
  • C. Rose and G. Wei. Eigenvalue estimates under Kato-type Ricci curvature conditions. 2020. arXiv
  • C. Rose. Almost positive Ricci curvature in Kato sense - an extension of Myers' theorem. 2019. 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

Articles in peer-reviewed journals

  • 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

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

12/2020 - Postdoc, Universität Potsdam
10/2018-09/2020     Postdoc, Max Planck Institute for Mathematics in the Sciences, Leipzig
06/2014-08/2014PhD student, Technische Universität Chemnitz
10/2009-05/2014Undergrad Studies in Mathematics, Technische Universität Chemnitz