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PD Dr. Martin Kell

Kontakt / Contact information

Fachbereich Mathematik
Universität Tübingen
Auf der Morgenstelle 10
72076 Tübingen
Germany

Tel: +49-(0)7071/29-7 62 18
Email
Raum: C 6 P 34

ORCID iD iconorcid.org/0000-0003-2875-2864

Lebenslauf / CV

Sprechstunde / Office hours - open door policy or via appointment

 

Forschungsinteressen / Research interests

    • Interplay of Geometry and Analysis
    • Generalized Curvature
    • Geometric Flows
    • Curvature and Isoperimetry

    Aktuelle Forschung / Current research

    Currently, one of my main target is to understand metric spaces whose Sobolev spaces are not Hilbert spaces. Those spaces can be seen as generalizations of Finsler manifolds. One distinguished property is that the natural heat flow and the Laplacian are non-linear.  Whereas many results are known for Riemannian-like metric spaces, called infinitesimally Hilbertian, very few results are known for spaces with non-linear infinitesimal structure. A first approach is to find a sectional curvature analogue similar to Alexandrov curvature. Convexity of the distance can be seen as a non-positive curvature. Currently, I'm trying to obtain a meaningful notion of non-negative curvature which hopefully gives a Finslerian version of Alexandrov spaces with curvature bounded from below.

    Wissenschaftliche Veröffentlichungen / Publications

    1. (with Kapovitch, V., Ketterer, Chr.) On the structure of RCD spaces with upper curvature bounds, preprint 2019 arXiv.
    2. (with Suhr, S.) On the existence of dual solutions for Lorentzian cost functions, Annales de l'Institut Henri Poincare / Analyse non lineaire accepted 2019. (preprint 2018 arXiv)
    3. (with Galaz-García, F., Mondino, A., Sosa, G.) On quotients of spaces with Ricci curvature bounded below, Journal of Functional Analysis 275(6) September 2018. (preprint arXiv)
    4. Transport maps, non-branching sets of geodesics and measure rigidity, Advances in Mathematics 320, November 2017. (preprint up-to-date or older on arXiv)
    5. (with Mondino, A.) On the volume measure of non-smooth spaces with Ricci curvature bounded below Annali della Scuola Normale Superiore di Pisa Vol XVII (2), April 2018. (preprint arXiv)
    6. Symmetric orthogonality and contractive projections in metric spaces, manuscripta mathematica Online First (2018) (preprint arXiv)
    7. Sectional curvature-type conditions on metric spaces, Journal of Geometric Analysis 29(1) January 2018. (preprint up-to-date or older on arXiv)
    8. On Cheeger and Sobolev differentials in metric measure spaces Revista Matemática Iberoamericana, Online first (2019) (preprint arXiv).
    9. Uniformly convex metric spaces Analysis and Geometry of Metric Spaces 2(1), December 2014. (preprint arXiv)
    10. (with Bačák, M., Hua, B., Jost, J., Schikorra, A.) A notion of nonpositive curvature for general metric spaces Differential Geometry and its Applications 38, November 2015. (preprint arXiv)
    11. q-heat flow and the gradient flow of the Renyi entropy in the p-Wasserstein space, Journal of Functional Analysis 271(8) October 2016. (preprint arXiv)
    12. On Interpolation and Curvature via Wasserstein Geodesics, Advances in Calculus of Variations 10(2), April 2017. (preprint arXiv)
    13. Dissertation - On curvature conditions using Wasserstein spaces - University of Leipzig Juli 2014 (at Qucosa).
    14. (with Jost, J., Rodrigues, Chr. S.) Representation of Markov chains by random maps: existence and regularity conditions, Calculus of Variations and Partial Differential Equations 54(3), November 2015. (preprint arXiv)
    15. Conley index of isolated equilibria Topological Methods In Nonlinear Analysis 38(2), December 2011.
    16. Diplomarbeit - Conley index of isolated equilibria - University of Rostock August 2010.

    Andere Veröffentlichungen / Not intended for publication