Christian Ketterer - Personal Webpage

Christian Ketterer

Department of Mathematics
University of Toronto
Room 6290
40 St George St

Email: ckettere(at)math(dot)toronto(dot)edu
Office: PG300 (PGB - 45 St. George St.)

Welcome!

This is my personal webpage. I am a postdoc in the Mathematics Department of the University of Toronto. My supervisors are Robert Haslhofer, Vitali Kapovitch and Robert McCann. I received my Phd at the Institute for Applied Mathematics at the University of Bonn under the supervision of Karl-Theodor Sturm. Click here for a recent CV.

Teaching

This fall I teach MAT351 Partial differential equations.

Research Interests

My current research is focused on geometric and analytic consequences of lower Ricci curvature bounds for metric measure space. This includes rigidity and almost rigidity statements, stability properties under measured Gromov-Hausdorff convergence, geometric constructions, topology, local structure and regularity. Lower Ricci curvature is understood in the sense of Lott, Sturm and Villani, but often also enforced by the so-called infinitesimal Hilbertianity that yields the celebrated RCD condition for metric measure spaces. More recently I also became interested in corresponding questions for Riemannian manifolds with lower Scalar curvature bounds.

Click here for a short exposition on my research interests and previous contributions.

Preprints

1. Stability of metric measure spaces with integral Ricci curvature bounds, preprint [arxiv | pdf]
2. On gluing Alexandrov spaces with lower Ricci curvature bounds (joint with Vitali Kapovitch and Karl-Theodor Sturm), preprint [arxiv | pdf]
3. On the structure of RCD spaces with upper curvature bounds (joint with Vitali Kapovitch and Martin Kell), preprint [arxiv | pdf]
4. Evolution variational inequality and Wasserstein control in variable curvature context, preprint [arxiv | pdf]

Articles

1. 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]
2. 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 | pdf]
3. The Heintze-Karcher inequality for metric measure spaces, Proc. Americ. Math. Soc. 148 (2020), no. 9, 4041-4056 [journal | pdf]
4. Stratified spaces and synthetic Ricci curvature bounds (joint with Jerome Bertrand, Ilaria Mondello and Thomas Richard), accepted in Annales l'Institut Fourier [arxiv | pdf]
5. Weakly noncollapsed RCD spaces with upper curvature bounds (joint with Vitali Kapovitch), Anal. Geom. Metr. Spaces 7 (2019), no. 1, 197-211 [journal | pdf]
6. CD meets CAT (joint with Vitali Kapovitch), J. Reine Angew. Math., https://doi:10.1515/crelle-2019-0021. [journal | pdf]
7. Rigidity for the spectral gap of $RCD(K,\infty)$-spaces (joint with Nicola Gigli, Kazumasa Kuwada, Shin-ichi Ohta), Amer. J. Math. (accepted) [journal | pdf]
8. Lagrangian calculus for non-symmetric diffusion operators, Adv. Calc. Var. , https://doi.org/10.1515/acv-2018-0001 [journal | pdf]
9. Sectional and intermediate Ricci curvature lower bounds via Optimal Transport (joint with Andrea Mondino), Adv. Math. 329:781-818, 2018 [journal | pdf]
10. On the geometry of metric measure spaces with variable curvature bounds, J. Geom. Anal. 27 (2017) no.3, 1951-1994 [journal | pdf]
11. Obata's Rigidity Theorem for Metric Measure Spaces, Anal. Geom. Metr. Spaces 3, 278-295, 2015 [journal | pdf]
12. 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 | pdf]
13. Cones over metric measure spaces and the maximal diameter theorem, J. Math. Pures Appl. (9) 103 (2015), no. 5, 1228-1275 [journal | pdf]
14. Ricci curvature bounds for warped products, J. Funct. Anal. 265(2): 266-299, 2013. [journal | pdf]

Slides

• Find here the slides of my talk on The Heintze-Karcher inequality for metric measure spaces in the MMS&Convergence Seminar organized by Raquel Perales.

Grants

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