| Private Homepage | https://sites.google.com/view/hhein/home |
| Research Interests | Kähler geometry Einstein metrics, Ricci flow Geometry and analysis on singular spaces Elliptic PDEs, singular perturbations and asymptotics |
| Selected Publications | • Hein HJ Gravitational instantons from rational elliptic surfaces. Journal of the American Mathematical Society Vol. 25, 2012 online • Hein HJ, Sun S Compact Calabi-Yau manifolds with isolated conical singularities. Publications Mathématiques de L'IHÉS Vol. 126, 2017 online • Hein HJ, Tosatti V Higher-order estimates for collapsing Calabi-Yau metrics. Cambridge Journal of Mathematics Vol. 8, 2020 online • Hein HJ, LeBrun C Mass in Kähler Geometry. Communications in Mathematical Physics Vol. 347, 2016 online • Hein HJ, Naber A New logarithmic Sobolev inequalities and an epsilon-regularity theorem for the Ricci flow. Communications on Pure and Applied Mathematics Vol. 67, 2014 online |
| Project membership Mathematics Münster | B: Spaces and Operators B1: Smooth, singular and rigid spaces in geometry |
| Current Publications | • Biquard O, Hein HJ The renormalized volume of a 4-dimensional Ricci-flat ALE space. Journal of Differential Geometry Vol. 123, 2023 online • Hein HJ, Sun S, Viaclovsky J, Zhang R Nilpotent structures and collapsing Ricci-flat metrics on the K3 surface. Journal of the American Mathematical Society Vol. 2022, 2022 online • Conlon R, Hein HJ Classification of asymptotically conical Calabi-Yau manifolds. , 2022 online • Hein HJ, Rasdeaconu R, Suvaina I On the classification of ALE Kähler manifolds. International Mathematics Research Notices Vol. 2021, 2021 online • Hein HJ, Tosatti V Smooth asymptotics for collapsing Calabi-Yau metrics. , 2021 online • Hein HJ, Sun S, Viaclovsky J, Zhang R Gravitational instantons and del Pezzo surfaces. , 2021 online • Fu X, Hein HJ, Jiang X Asymptotics of Kähler-Einstein metrics on complex hyperbolic cusps. , 2021 online • Hein HJ, Tosatti V Higher-order estimates for collapsing Calabi-Yau metrics. Cambridge Journal of Mathematics Vol. 8, 2020 online • Hein HJ A Liouville theorem for the complex Monge-Ampère equation on product manifolds. Communications on Pure and Applied Mathematics Vol. 72, 2019 online |
| Current Projects | • CRC 1442: Geometry: Deformation and Rigidity - B05: Scalar curvature in Kähler geometry In this project we propose to study the degeneration of Kähler manifolds with constant or bounded scalar curvature under a non-collapsing assumption. For Riemannian manifolds of bounded sectional curvature, this is the content of the classical Cheeger-Gromov convergence theory from the 1970s. For Riemannian manifolds of bounded Ricci curvature, definitive results were obtained by Cheeger-Colding-Naber in the past 10-20 years, with spectacular applications to the Kähler-Einstein problem on Fano manifolds. Very little is currently known under only a scalar curvature bound even in the Kähler case. We propose to make progress in two different directions: (I) Gather examples of weak convergence phenomena related to the stability of the Positive Mass Theorem for Kähler metrics and to Taubes' virtually infinite connected sum construction for ASD 4-manifolds. (II) Study uniqueness and existence of constant scalar curvature Kähler metrics on non-compact or singular spaces by using direct PDE methods. online • EXC 2044 - B1: Smooth, singular and rigid spaces in geometry Many interesting classes of Riemannian manifolds are precompact in the Gromov-Hausdorfftopology. The closure of such a class usually contains singular metric spaces. Understanding thephenomena that occur when passing from the smooth to the singular object is often a first step toprove structure and finiteness results. In some instances one knows or expects to define a smoothRicci flow coming out of the singular objects. If one were to establishe uniqueness of the flow, thedifferentiable stability conjecture would follow. If a dimension drop occurs from the smooth to thesingular object, one often knows or expects that the collapse happens along singular Riemannianfoliations or orbits of isometric group actions. Rigidity aspects of isometric group actions and singular foliations are another focus in this project.For example, we plan to establish rigidity of quasi-isometries of CAT(0) spaces, as well as rigidity oflimits of Type III Ricci flow solutions and of positively curved manifolds with low-dimensional torusactions.We will also investigate area-minimising hypersurfaces by means of a canonical conformal completionof the hypersurface away from its singular set. online | hhein@uni-muenster.de |
| Phone | +49 251 83-33722 |
| FAX | +49 251 83-32711 |
| Room | 406 |
| Secretary | Sekretariat Huppert Frau Sandra Huppert Telefon +49 251 83-33748 Fax +49 251 83-32711 Zimmer 411 |
| Address | Prof. Dr. Hans-Joachim Hein Mathematisches Institut Fachbereich Mathematik und Informatik der Universität Münster Einsteinstrasse 62 48149 Münster Deutschland |
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