| 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, Tosatti V Higher-order estimates for collapsing Calabi-Yau metrics. Cambridge Journal of Mathematics Vol. 8, 2020 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 • Biquard O, Hein HJ The renormalized volume of a 4-dimensional Ricci-flat ALE space. Journal of Differential Geometry Vol. 123, 2023 online • Conlon RJ, Hein HJ Classification of asymptotically conical Calabi-Yau manifolds. Duke Mathematical Journal Vol. 173 (5), 2024 online |
| Topics in Mathematics Münster | T6: Singularities and PDEs T7: Field theory and randomness |
| Current Publications | • Hein, Hans-Joachim; Lee, Man-Chun; Tosatti, Valentino Collapsing immortal Kähler-Ricci flows. Forum of Mathematics Pi Vol. 13, 2025 online • Hein, HJ; Tosatti, V Smooth asymptotics for collapsing Calabi-Yau metrics. Communications on Pure and Applied Mathematics Vol. 78 (2), 2025 online • Hein, HJ; Sun, S; Viaclovsky, J; Zhang, R Asymptotically Calabi metrics and weak Fano manifolds. Geometry and Topology Vol. 29 (5), 2025 online • Fu, Xin; Hein, Hans-Joachim; Jiang, Xumin A continuous cusp closing process for negative Kähler-Einstein metrics. Geometric And Functional Analysis Vol. 35, 2025 online • Conlon RJ, Hein HJ Classification of asymptotically conical Calabi-Yau manifolds. Duke Mathematical Journal Vol. 173 (5), 2024 online • Biquard O, Hein HJ The renormalized volume of a 4-dimensional Ricci-flat ALE space. Journal of Differential Geometry Vol. 123, 2023 online • Fu X, Hein HJ, Jiang X Asymptotics of Kähler-Einstein metrics on complex hyperbolic cusps. Calculus of Variations and Partial Differential Equations Vol. 63 (1), 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 • Hein HJ, Rasdeaconu R, Suvaina I On the classification of ALE Kähler manifolds. International Mathematics Research Notices Vol. 2021, 2021 online |
| Current Projects | • EXC 2044 - T06: Singularities and PDEs Our goal is to utilise and further develop the theory of non-linear PDEs to understand singular phenomena arising in geometry and in the description of the physical world. Particular emphasis is put on the interplay of geometry and partial differential equations and also on the connection with theoretical physics. The concrete research projects range from problems originating in geometric analysis such as understanding the type of singularities developing along a sequence of four-dimensional Einstein manifolds, to problems in evolutionary PDEs, such as the Einstein equations of general relativity or the Euler equations of fluid mechanics, where one would like to understand the formation and dynamics (in time) of singularities. online • EXC 2044 - T07: Field theory and randomness Quantum field theory (QFT) is the fundamental framework to describe matter at its smallest length scales. QFT has motivated groundbreaking developments in different mathematical fields: The theory of operator algebras goes back to the characterisation of observables in quantum mechanics; conformal field theory, based on the idea that physical observables are invariant under conformal transformations of space, has led to breakthrough developments in probability theory and representation theory; string theory aims to combine QFT with general relativity and has led to enormous progress in complex algebraic geometry, among others. online • CRC 1442 - B05: Scalar curvature between Kähler and spin This project aims to connect recent developments in Kähler geometry and spin geometry related to lower scalar curvature bounds and the Positive Mass Theorem. We would like to sharpen the Cecchini-Zeidler bandwidth inequality in the case of Kähler metrics and to find new proofs and extensions of the Positive Mass Theorem. One setting of interest is the case of spin^c manifolds equipped with almost-Kähler metrics, particularly in real dimension 4. • CRC 1442 - B06: Einstein 4-manifolds with two commuting Killing vectors We will investigate the existence, rigidity and classification of 4-dimensional Lorentzian and Riemannian Einstein metrics with two commuting Killing vectors. Our goal is to address open questions in the study of black hole uniqueness and gravitational instantons. In the Ricci-flat case, the problem reduces to the analysis of axisymmetric harmonic maps from R^3 to the hyperbolic plane. In the case of negative Ricci curvature, a detailed understanding of the conformal boundary value problem for asymptotically hyperbolic Einstein metrics is required. • 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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