Research Interests

Research Interests

$\bullet$ Kähler geometry
$\bullet$ Einstein metrics, Ricci flow
$\bullet$ Geometry and analysis on singular spaces
$\bullet$ 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

Current Cluster Publications

Current Cluster Publications of Prof. Dr. Hans-Joachim Hein

$\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, January 2024. doi:10.1215/00127094-2023-0030.

$\bullet $ Xin Fu, Hans-Joachim Hein, and Xumin Jiang. A continuous cusp closing process for negative Kähler-Einstein metrics. arXiv e-prints, January 2024. arXiv:2401.11468.

$\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, Song Sun, Jeff Viaclovsky, and Ruobing Zhang. Gravitational instantons and del Pezzo surfaces. arXiv e-prints, November 2021. arXiv:2111.09287.

$\bullet $ Xin Fu, Hans-Joachim Hein, and Xumin Jiang. Asymptotics of Kähler-Einstein metrics on complex hyperbolic cusps. arXiv e-prints, August 2021. arXiv:2108.13390.

$\bullet $ Hans-Joachim Hein, Rares Rasdeaconu, and Ioana Suvaina. On the classification of ALE Kähler manifolds. International Mathematics Research Notices, 2021(14):10957–10980, July 2021. doi:10.1093/imrn/rnz376.

$\bullet $ Hans-Joachim Hein and Valentino Tosatti. Smooth asymptotics for collapsing calabi-yau metrics. arXiv e-prints, February 2021. arXiv:2102.03978.

$\bullet $ Hans-Joachim Hein and Valentino Tosatti. Higher-order estimates for collapsing Calabi-Yau metrics. Cambridge Journal of Mathematics, 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.