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, Tosatti V Higher-order estimates for collapsing Calabi-Yau metrics. Cambridge Journal of Mathematics Vol. 8, 2020 online
Hein HJ, Sun S Compact Calabi-Yau manifolds with isolated conical singularities. Publications Mathématiques de L'IHÉS Vol. 126, 2017 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
Hein HJ Gravitational instantons from rational elliptic surfaces. Journal of the American Mathematical Society Vol. 25, 2012 online

Current Publications

Current Publications

$\bullet$ Ronan J. Conlon and Hans-Joachim Hein. Classification of asymptotically conical Calabi-Yau manifolds. arXiv e-prints, January 2022. arXiv:2201.00870.

$\bullet$ 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.