Research Interests
$\bullet$ Kähler geometry
$\bullet$ Einstein metrics, Ricci flow
$\bullet$ Geometry and analysis on singular spaces
$\bullet$ Elliptic PDEs, singular perturbations and asymptotics
• 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
Recent Publications of Prof. Dr. Hans-Joachim Hein
$\bullet $ Xin Fu, Hans-Joachim Hein, and Xumin Jiang. A continuous cusp closing process for negative Kähler-Einstein metrics. Geometric and Functional Analysis, 35(2):542–632, March 2025. doi:10.1007/s00039-025-00708-y.
$\bullet $ Hans‐Joachim Hein and Valentino Tosatti. Smooth asymptotics for collapsing Calabi–Yau metrics. Communications on Pure and Applied Mathematics, 78(2):382–499, February 2025. doi:10.1002/cpa.22228.
$\bullet $ Hans-Joachim Hein, Man-Chun Lee, and Valentino Tosatti. Collapsing immortal Kähler-Ricci flows. arXiv e-prints, May 2024. arXiv:2405.04208.
$\bullet $ Ronan J. Conlon and Hans-Joachim Hein. Classification of asymptotically conical Calabi-Yau manifolds. Duke Mathematical Journal, April 2024. doi:10.1215/00127094-2023-0030.
$\bullet $ X. Fu, H.-J. Hein, and X. Jiang. Asymptotics of Kähler-Einstein metrics on complex hyperbolic cusps. Calculus of Variations and Partial Differential Equations, November 2023. doi:10.1007/s00526-023-02613-4.
$\bullet $ Olivier Biquard and Hans-Joachim Hein. The renormalized volume of a 4-dimensional Ricci-flat ALE space. Journal of Differential Geometry, 123(3):411–429, March 2023. doi:10.4310/jdg/1683307004.
$\bullet $ Hans-Joachim Hein, Song Sun, Jeff Viaclovsky, and Ruobing Zhang. Nilpotent structures and collapsing Ricci-flat metrics on the K3 surface. J. Am. Math. Soc., 35(1):123–209, January 2022. doi:10.1090/jams/978.
$\bullet $ Hans-Joachim Hein, Rares Rasdeaconu, and Ioana Suvaina. On the classification of ALE Kähler manifolds. Int. Math. Res. Notices, 2021(14):10957–10980, July 2021. doi:10.1093/imrn/rnz376.
$\bullet $ Hans-Joachim Hein and Valentino Tosatti. Higher-order estimates for collapsing Calabi-Yau metrics. Camb. J. Math., 8:683–773, December 2020. doi:10.4310/cjm.2020.v8.n4.a1.
$\bullet $ Hans-Joachim Hein. A Liouville theorem for the complex Monge-Ampère equation on product manifolds. Commun. Pure Appl. Math., 72(1):122–135, January 2019. doi:10.1002/cpa.21751.