Christian Ketterer - Personal Webpage

Christian Ketterer

Welcome!

Christian Ketterer

This is my personal webpage. Currently I am Vertretungsprofessor for Differential Geometry in the Department of Mathematics at the University of Freiburg.

Click here for a recent CV.

You can find me on arXiv, Google Scholar, zbMath.org and MathSciNet.




Mailing adress:Christian Ketterer
Mathematisches Institut
Abt. für Reine Mathematik
Albert-Ludwigs-Universität Freiburg
Ernst-Zermelo-Str. 1
79104 Freiburg, Germany
Email: christian.ketterer@math.uni-freiburg.de
Raum: Ernst-Zermelo-Str. 1, Raum 337
Telefon: (+49) 761-203-5654


Lehre (Teaching)



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Research Interests

My research is about geometric and analytic consequences of synthetic lower curvature bounds for metric and metric measure space. This includes rigidity and almost rigidity statements, stability properties under measured Gromov-Hausdorff convergence, geometric constructions, topology, local structure and regularity.

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Preprints

  1. The rigidity of sharp spectral gap in nonnegatively curved spaces (joint with Yu Kitabeppu and Sajjad Lakzian), preprint [arxiv]
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Articles

  1. Rigidity of mean convex subsets in non-negatively curved RCD spaces and stability of mean curvature bounds, accepted in J. Analysis and Topology [arxiv]
  2. On the structure of RCD spaces with upper curvature bounds (joint with Vitali Kapovitch and Martin Kell), Math. Zeitschrift., 301, 3469-3502 (2022) [journal]
  3. Stability of metric measure spaces with integral Ricci curvature bounds, J. Funct. Anal. , vol 281, Issue 8, 2021, 109142 [journal]
  4. On gluing Alexandrov spaces with lower Ricci curvature bounds (joint with Vitali Kapovitch and Karl-Theodor Sturm), accepted in Comm. Anal. and Geom. [arxiv]
  5. Inscribed radius bounds for lower ricci bounded metric measure spaces with mean convex boundary (joint with Annegret Burtscher, Robert McCann and Eric Woolgar), SIGMA Symmetry Integrability Geom. Methods Appl. 16 (2020), Paper No. 131, 29 pp. [journal]
  6. Stability of graphical tori with almost nonnegative scalar curvature (joint with Armando J. Cabrera Pacheco and Raquel Perales), Calc. Var. Partial Differential Equations 59 (2020), no. 4, 134 [journal]
  7. The Heintze-Karcher inequality for metric measure spaces, Proc. Americ. Math. Soc. 148 (2020), no. 9, 4041-4056 [journal]
  8. Stratified spaces and synthetic Ricci curvature bounds (joint with Jerome Bertrand, Ilaria Mondello and Thomas Richard), Annales l'Institut Fourier, Volume 71 (2021) no. 1, pp. 123-173. [journal]
  9. Weakly noncollapsed RCD spaces with upper curvature bounds (joint with Vitali Kapovitch), Anal. Geom. Metr. Spaces 7 (2019), no. 1, 197-211 [journal]
  10. CD meets CAT (joint with Vitali Kapovitch), J. Reine Angew. Math., https://doi:10.1515/crelle-2019-0021. [journal]
  11. Rigidity for the spectral gap of $RCD(K,\infty)$-spaces (joint with Nicola Gigli, Kazumasa Kuwada, Shin-ichi Ohta), Amer. J. Math. 142 (2020), no. 5, 1559–1594 [journal]
  12. Lagrangian calculus for non-symmetric diffusion operators, Adv. Calc. Var. , https://doi.org/10.1515/acv-2018-0001 [journal]
  13. Sectional and intermediate Ricci curvature lower bounds via Optimal Transport (joint with Andrea Mondino), Adv. Math. 329:781-818, 2018 [journal]
  14. On the geometry of metric measure spaces with variable curvature bounds, J. Geom. Anal. 27 (2017) no.3, 1951-1994 [journal]
  15. Obata's Rigidity Theorem for Metric Measure Spaces, Anal. Geom. Metr. Spaces 3, 278-295, 2015 [journal]
  16. Failure of topological splitting and topological maximal diameter theorems for $MCP$-spaces (joint with Tapio Rajala), Potential Anal. 42 (2015) , no.3, 645-655 [journal]
  17. Cones over metric measure spaces and the maximal diameter theorem, J. Math. Pures Appl. (9) 103 (2015), no. 5, 1228-1275 [journal]
  18. Ricci curvature bounds for warped products, J. Funct. Anal. 265(2): 266-299, 2013. [journal]
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Slides

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Other publications

  • Evolution variational inequality and Wasserstein control in variable curvature context, preprint [arxiv | pdf]
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    Thesis

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    Lecture notes

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    Grants

    DFG research fellowship DFGlogo
    "Synthetische Kruemmungsschranken durch Methoden des optimal Transports", Projekt-Nr. 396662902

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    Some photos

    Christian Ketterer Christian Ketterer


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