Christian Ketterer - Personal Webpage

# Welcome!

 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. Click this link to get to my University of Freiburg webpage 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) 0761 203 5563

### 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.

### Preprints

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

### Articles

 Rigidity of mean convex subsets in non-negatively curved RCD spaces and stability of mean curvature bounds, accepted in J. Analysis and Topology [arxiv] On the structure of RCD spaces with upper curvature bounds (joint with Vitali Kapovitch and Martin Kell), Math. Zeitschrift., 301, 3469-3502 (2022) [journal] Stability of metric measure spaces with integral Ricci curvature bounds, J. Funct. Anal. , vol 281, Issue 8, 2021, 109142 [journal] On gluing Alexandrov spaces with lower Ricci curvature bounds (joint with Vitali Kapovitch and Karl-Theodor Sturm), accepted in Comm. Anal. and Geom. [arxiv] 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] 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] The Heintze-Karcher inequality for metric measure spaces, Proc. Americ. Math. Soc. 148 (2020), no. 9, 4041-4056 [journal] 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] Weakly noncollapsed RCD spaces with upper curvature bounds (joint with Vitali Kapovitch), Anal. Geom. Metr. Spaces 7 (2019), no. 1, 197-211 [journal] CD meets CAT (joint with Vitali Kapovitch), J. Reine Angew. Math., https://doi:10.1515/crelle-2019-0021. [journal] 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] Lagrangian calculus for non-symmetric diffusion operators, Adv. Calc. Var. , https://doi.org/10.1515/acv-2018-0001 [journal] Sectional and intermediate Ricci curvature lower bounds via Optimal Transport (joint with Andrea Mondino), Adv. Math. 329:781-818, 2018 [journal] On the geometry of metric measure spaces with variable curvature bounds, J. Geom. Anal. 27 (2017) no.3, 1951-1994 [journal] Obata's Rigidity Theorem for Metric Measure Spaces, Anal. Geom. Metr. Spaces 3, 278-295, 2015 [journal] 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] Cones over metric measure spaces and the maximal diameter theorem, J. Math. Pures Appl. (9) 103 (2015), no. 5, 1228-1275 [journal] Ricci curvature bounds for warped products, J. Funct. Anal. 265(2): 266-299, 2013. [journal]

### Slides

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

### Other publications

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