Address:

Universität Duisburg-Essen

Fakultät für Mathematik

Thea-Leymann-Straße 9

45127 Essen

Email: heiko.kroener@uni-due.de

Current position:

After my phd in 2012 in Heidelberg, I spent several postdoc years within Germany, at University of Tuebingen,

WIAS Berlin, University of Hamburg and University of Freiburg. Since August 2019 I am a postdoc in Professor Paola Pozzi's DFG

Project: Flow of elastic networks

Research interests: Analysis of PDE, Numerical Analysis of PDE

Publications:

1) H. Kröner: A note on inverse mean curvature flow in cosmological spacetimes, Math. Nachr. 287, No. 2-3, 290-296 (2014)

2) H. Kröner: Approximative Green's functions on surfaces and pointwise error estimates for the finite element method, Comput. Methods Appl. Math. 17, No 1, 51-64 (2017)

3) H. Kröner: Approximation rates for regularized level set power mean curvature flow, Port. Math. (N. S.) 74, No. 2, 115-126 (2017)

4) H. Kröner: Inverse curvature flows in asymptotically Robertson Walker spacetimes, J. Differ. Equations 264, No. 7, 4303-4342 (2018)

5) M. Hermann, R. Herzog, H. Kröner, S. Schmidt, J. Vidal: Analysis and an interior-point approach for TV image reconstruction on smooth surfaces, SIAM J. Imaging Sci. 11, No. 2, 889-922 (2018)

6) A. Kröner, E. Kröner, H. Kröner: Finite element approximation of level set motion by powers of the mean curvature, SIAM J. Sci. Comput. 40, No. 6, A4158-A4183 (2018)

7) H. Kröner: A note on expansion of convex plane curves via inverse curvature flow, NoDEA, Nonlinear Differ. Equ. Appl. 26, No. 2, Paper No. 9, 11 pages (2019)

8) H. Kröner, J. Scheuer: Expansion of pinched hypersurfaces of the Euclidean and hyperbolic space by high powers of curvature, Math. Nachr. 292, No. 7, 1514-1529 (2019)

9) H. Kröner: Analysis of constants in error estimates for the finite element approximation of regularized nonlinear geometric evolution equations, SIAM J. Numer. Anal. 57, No. 5, 2413-2435 (2019)

10) H. Kröner: Non-collapsing in homogeneity greater than one via a two-point method for a special case, Proc. R. Soc. Edinb., Sect. A, Math., 149, No. 6, 1627-1635 (2019)

11) A. A. Ali, M. Hinze, H. Kröner: Optimal control of elliptic surface PDEs with pointwise bounds on the state, IMA J. Numer. Anal., Vol. 40 (1), 2020. 

12) P. Bryan, J. Scheuer, H. Kröner: Li-Yau gradient estimates for curvature flows in positively curved manifolds, Methods and Applications of Analysis, accepted, arXiv:1901.09763v1

13) H. Kröner: Flowing the leaves of a foliation with normal speed given by the logarithm of general curvature functions, JFA, accepted, arXiv:1706.02976v2, 

14) H. Kröner, M. Novaga, P. Pozzi: Anisotropic curvature flow of immersed networks, Milan Journal of Mathematics, accepted, arXiv:2012.02490

15) A. Kröner, H. Kröner: Hyperplane separation type theorems in Hadamard manifolds, Journal of Convex Analysis, accepted.

16)  A. Kröner, H. Kröner: A priori error estimates for finite element approximations of regularized level set flows in higher norms,  arXiv:2003.01017 , Applied Numerical Mathematics, accepted

17) A. Cesaroni, H. Kröner, M. Novaga: Anisotropic mean curvature flow of Lipschitz graphs and convergence to self-similar solutions, arXiv:2105.06359  , ESAIM: COCV, accepted

Preprints:

18) H. Kröner: Definition and certain convergence properties of a two-scale method for Monge-Ampere type equations,  arXiv:1912.03405v1

19) A. Cesaroni, H. Kröner, M. Novaga: Graphical translators for anisotropic and crystalline mean curvature flow, arXiv:2107.12082 [math.AP]

Selected workshops:

Oberwolfach-Workshop: Partial Differential Equations, 2007

Invited speaker at the Analysis and Numerics in Curvature energies-Meeting, 2016

Oberwolfach-Workshop: Emerging Developments in Interfaces and Free Boundaries, 2017
 

Awards/Fellowships:

First prize in the second round of the German national competition in mathematics for high school students (Bundeswettbewerb Mathematik)

2005 to 2007: Scholarship of the German National Academic Foundation (Studienstiftung des Deutschen Volkes)

2014: Postdoctoral Fellowship of the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) in Berlin