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
Hein HJ, Sun S. Compact Calabi-Yau manifolds with isolated conical singularities. Publications mathématiques de l'IHÉS, Vol. 126, 2017
Hein HJ, Tosatti V. Higher-order estimates for collapsing Calabi-Yau metrics. Cambridge Journal of Mathematics, Vol. 8, 2020
Hein HJ, LeBrun C. Mass in Kähler Geometry. Communications in Mathematical Physics, Vol. 347, 2016
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

Current Publications

$\bullet $ X. Fu, H.-J. Hein, and X. Jiang. Asymptotics of Kähler-Einstein metrics on complex hyperbolic cusps. arXiv e-prints, August 2021. arXiv:2108.13390.

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

$\bullet $ H.-J. Hein and V. Tosatti. Smooth asymptotics for collapsing calabi-yau metrics. arXiv e-prints, February 2021. arXiv:2102.03978.