Publications

Monographs

Moduli Spaces of Riemannian Metrics. (with D.J. Wraith) Oberwolfach Seminars Vol. 46, Birkhäuser, Basel 2015.
Endlichkeitssätze und positive Krümmung. Habilitation thesis. MPI MIS Lecture Notes Series 9, Leipzig 2000.
Sofia Kowalewskaja. (with P. Hawig) Scientific biography of the Russian mathematician and author S. W. Kowalewskaja (1850-1891). Birkhäuser, Basel 1993.

Editorships

Differential geometry in the large. Proceedings of the Australian-German workshop on differential geometry in the large, Creswick, Australia, February 4–15, 2019. (with O. Dearricott, Y. Nikolayevsky, T. Leistner, D. Crowley) London Mathematical Society Lecture Note Series 463. Cambridge: Cambridge University Press (2021).
Topics in metric Riemannian geometry. (with F. Fang, X. Rong, Y. Yang) Front. Math. China 11, No. 5, Special Issue. Beijing-Berlin-Heidelberg: Springer/Higher Education Press (2016).

Book Chapters

Collapsing and Almost Nonnegative Curvature. In: Bär, Lohkamp and Schwarz, Global Differential Geometry, Springer Proceedings in Mathematics 17, 93-106 (2012)

Research Articles

Moduli Spaces of Nonnegatively Curved Metrics on Closed Manifolds and RCD spaces
To appear in Springer Tohoku Series in Mathematics , (PDF) (2024)
Moduli Spaces of Metrics with Lower or Pinched Curvature Bounds and their Compactifications
To appear in Journal of Mathematical Study (PDF) (2024)
Categorical and geometric methods in statistical, manifold, and machine learning (with H.-V. Lê, H.-Q. Minh, F. Protin)
To appear in Springer Tohoku Series in Mathematics , (PDF) (2024)
On the topology of moduli spaces of non-negatively curved Riemannian metrics (with M. Wiemeler)
Mathematische Annalen 384, No. 3-4, 1629-1651 (2022)
Stability of the Cut Locus and a Central Limit Theorem for Fréchet Means of Riemannian Manifolds (with B. Eltzner, F. Galaz-Garcia, S. F. Huckemann)
Proc. Amer. Math. Soc. 149 (2021), 3947-3963, https://doi.org/10.1090/proc/15429 (2021)
Epidemic Dynamics via Wavelet Theory and Machine Learning, with Applications to Covid-19 (with Frédéric Protin, Hông Vân Lê et al.), Biology 2020 9(12), https://doi.org/10.3390/biology9120477 (2020)
Finiteness and realization theorems for Alexandrov spaces with bounded curvature (with F. Galaz-Garcia) Bol. Soc. Mat. Mex., III. Ser. 26, No. 2, 749-756 (2020)
Smooth stability and sphere theorems for manifolds and Einstein manifolds with positive scalar curvature (with M. Wiemeler) Communications in Analysis and Geometry 27, no. 2, 491-509 (2019)
On the Torsion in the Center Conjecture (with V. Kapovich and A. Petrunin) Electronic Research Announcements in Mathematical Sciences 25, 27-35 (2018)
Nonconnected Moduli Spaces of Nonnegative Sectional Curvature Metrics on Simply Connected Manifolds. (with A. Dessai and S. Klaus) Bull. London Math. Soc. 50, 96–107 (2018)
Spaces and moduli spaces of Riemannian metrics. Front. Math. China 11, no. 5, 1335–1343 (2016)
Fiber-Bragg Gitter basierte Formsensorik in der Ureterorenoskopie - Konstruktion und Test eines Ausführungskonzeptes. (with H. Pauer, D. Teber und H. Woern) In: Tagungsband der 15. Jahrestagung der Deutschen Gesellschaft für Computer- und Roboterassistierte Chirurgie (CURAC) (2016)
Towards 1-Component Bragg-Grating Based Shape Sensing. (with H. Pauer, M. Rosenberger, M. Girschikofsky, R. Hellmann, H. Woern) In: 19th International Conference on Information Fusion Heidelberg, Germany - July 5-8, 2016 (2016)
Shape Sensing Based on FBG-Technology - Extension of the Application Possibilities Due to Innovative Sensor-Configurations. (with H. Pauer, Chr. Ledermann, J. Raczkowsky, H. Woern) In: Navigation and Actuation of Flexible Instruments in Medical Applications (NAFIMA) Workshop Proceedings - IROS2015 (2015)
Pseudo-Data Generation Software for FBG-Optical Fiber Based Shape Sensing. (with H. Pauer, Chr. Ledermann, H. Woern) In: Proceedings - SENSOR 2015 (AMA Conferences), ISBN 978-3-9813484-8-4 (2015)
Validation of a Pseudo-Data-Generation-Software for FBG-Optical Fiber Based Shape Sensing. (with H. Pauer, Chr. Ledermann, L. Vojkovic, H. Woern) In: Proceedings Innovation Messtechnik 2015, ISBN 978-3-8440-3560-5 (2015)
Non-Linear Compensation of Production Inaccuracies and Material Drift by Adjusting the Sensor Data Fusion Algorithms for Shape Sensing Based on FBG-Optical Fibers. (with H. Pauer, Chr. Ledermann, H. Woern) In: Proceedings of the 2014 IEEE Ninth International Conference on Multisensor Fusion and Information Integration (MFI) (2014)
Consistent Quality Evaluation Method for Shape Sensors based on FBG–Optical Fibers Used in Minimally Invasive Surgery. (with H. Pauer, Chr. Ledermann, H. Woern) In: Proceedings of the 17. ITG / GMA Fachtagung Sensoren und Messsysteme, Editor VDE Verlag Berlin - Offenbach (2014)
Analyse der Anforderungen an Formsensoren zur Verwendung in der minimal-invasiven Chirurgie. (with H. Pauer, H. Kenngott, Chr. Ledermann, H. Woern) In: Tagungsband der 13. Jahrestagung der Deutschen Gesellschaft für Computer- und Roboterassistierte Chirurgie (CURAC) (2014)
Manifolds with almost nonnegative curvature operator and principal bundles. (with M. Herrmann and D. Sebastian) Annals of Global Analysis and Geometry, DOI10.1007/s10455-013-9372-2 (2013)
Collapsing and Almost Nonnegative Curvature. In: Bär, Lohkamp and Schwarz, Global Differential Geometry, Springer Proceedings in Mathematics 17, 93-106 (2012)
Nilpotency, Almost Nonnegative Curvature, and the Gradient Flow on Alexandrov Spaces. (with V. Kapovitch and A. Petrunin) Annals of Mathematics 171, 343–373 (2010)
Nonnegative Curvature and Cobordism Type. (with A. Dessai) Mathematische Zeitschrift, Z 257, no.1, 7–12 (2007)
Nonnegative Pinching, Homotopy Type and Bundles with infinitely many Souls. (with V. Kapovitch and A. Petrunin) Journal of Differential Geometry 71, 365–383 (2005)
Nonnegatively and Positively Curved Invariant Metrics on Circle Bundles. (with K. Shankar and K. Tapp) Proceedings of the A.M.S. 133, 2449-2459 (2005)
Metrics of Positive Ricci Curvature on Quotient Spaces. (with L. Schwachhöfer) Mathematische Annalen 330, 59–91 (2004)
Duality versus Dual Flatness in Quantum Information Geometry. (with N. Ay) Journal of Mathematical Physics 44, 1512–1518 (2003)
Geometric Diffeomorphism Finiteness in Low Dimensions and Homotopy Group Finiteness. Mathematische Annalen 322, 413–420 (2002)
Smooth Diameter and Eigenvalue Rigidity in Positive Ricci Curvature. Proceedings of the A.M.S. 130, 303–306 (2002)
Dually Flat Manifolds and Global Information Geometry. (with N. Ay) Open Systems and Information Dynamics 9, 195–200 (2002)
Asymptotical Flatness and Cone Structure at Infinity. (with A. Petrunin) Mathematische Annalen 321, 775–788 (2001)
Diffeomorphism Finiteness, Positive Pinching, and Second Homotopy. (with A. Petrunin) Geometric and Functional Analysis (GAFA) 9, 736–774 (1999)
Collapsing versus Positive Pinching. (with A. Petrunin and X. Rong) Geometric and Functional Analysis (GAFA) 9, 699–735 (1999)
Invariant Metrics of Positive Ricci Curvature on Principal Bundles. (with P. Gilkey and J.-H. Park) Mathematische Zeitschrift 227, 455-463 (1998)
Collapsing, Solvmanifolds and Infrahomogeneous Spaces. Differential Geometry and its Applications 7, 251–264 (1997)
On the Structure of Compact Simply Connected Manifolds of Positive Sectional Curvature. Geometriae Dedicata 67, 107–116 (1997)
Hausdorff Convergence and the Fundamental Group. Mathematische Zeitschrift 218, 207–211 (1995)
On the geometry of infrasolvmanifolds. (Zur Geometrie von Infrasolvmannigfaltigkeiten.) (German) Zbl 0885.53040, Bochum: Math. Fak., Univ. Bochum (1993)

Mathematics Conferences Proceedings

Sphere Theorems, Space Forms, and Positive Scalar Curvature. (with M. Wiemeler) Oberwolfach Reports 14(3), 2281-2283, European Mathematical Society Publishing House (2017)
Fundamentals of Geometry. Oberwolfach Reports 8(2), 999, European Mathematical Society Publishing House (2011)
Nilpotency and almost nonnegative curvature. Oberwolfach Reports 3(4), 2718-2721, European Mathematical Society Publishing House (2006)
Manifolds of positive Ricci curvature. Recent advances in geometry and topology, 385–390, Cluj University Press, Cluj-Napoca (2004)
Biquotients, curvature and homotopy Type. Oberwolfach Reports 1(4), 2509–2512, European Mathematical Society Publishing House (2004)
Hausdorff convergence and infrasolvmanifolds. Geometry and global analysis (Sendai, 1993), 387–397, Tohoku University Press, Sendai (1993)

Recent Preprints (on the arxiv)

Unified modelling of epidemics by coupled dynamics via Monte-Carlo Markov Chain algorithms (with Frédéric Protin, Hông Vân Lê et al.)

Further Preprints

Seifert Fiberings and Collapsing of Infrasolv Spaces (with O. Baues) (2012)
A note on nonnegative curvature and (rational) homotopy type (with A. Dessai) (2011)
Almost Nonnegative Curvature and Cohomogeneity One (with L. Schwachhöfer) (2001)

Education, Recreation, and Popularization

Albrecht Dürer als Mathematiker (2008)
Differentialgeometrie und Schwarze Löcher (1998)
Raymond Smullyan - Satan, Cantor and infinity, and other mind-boggling puzzles. Transl. from the English by Wilderich Tuschmann. (Satan, Cantor und die Unendlichkeit. Aus dem Englischen übersetzt von Wilderich Tuschmann.) (German) Birkhäuser, Basel (1993), Insel, Frankfurt/Leipzig (1997)