Publications and Preprints
Transgressive Harmonic Maps and SU(1,1) Self-Duality Solutions
(joint with Sebastian Heller and Hartmut Weiß)
This preprint establishes a duality between harmonic maps to hyperbolic and de Sitter 3-space. This duality extends to a class of maps into the 3-sphere, seen as the union of a two copies of hyperbolic 3-space glued along their boundaries at infinity. These maps are called transgressive harmonic maps and they correspond to solutions of the SU(1,1) self duality equation. We construct many examples of such harmonic maps and SU(1,1) self duality solutions by gluing. These maps induce tau-real negative sections of the Deligne–Hitchin moduli space, which are not twistor lines.
Topology of asymptotically conical Calabi–Yau and G2 manifolds and desingularization of nearly Kahler and nearly G2 conifolds
This article reports on obstructions to a gluing construction of nearly Kahler and nearly G2 manifolds. It is part of a larger project aimed at finding new inhomogeneous examples of such manifolds.
On limit spaces of Riemannian manifolds with volume and integral curvature bounds
This paper investigates potential limits of Riemannian manifolds with the Riemann tensor uniformly bounded in Lp, allowing local collapse. Using results of Shioya, it gives a particularly pleasant description of limit spaces of surfaces.
Homogeneous spinor flow (joint with Marco Freibert and Hartmut Weiß)
This work studies the spinor flow on homogeneous manifolds, where the parabolic PDE reduces to an ODE. A notable observation is that a certain nearly Kahler manifold is a globally stable critical point of the homogeneous spinor flow.
Blowup criteria for geometric flows on surfaces
This paper gives a general approach to blowup criteria for geometric flows on closed surfaces, based on parabolic regularity and compactness results tailored to potentially degenerating underlying geometries.
Stability of the spinor flow
This paper establishes stability near Ricci-flat special holonomy metrics for the spinor flow and gives a necessary condition in the volume-constrained setting.
Thesis
Long Time Behavior of the Spinor Flow
Christian-Albrechts-Universitat zu Kiel | May 2018 | link
The thesis was written under the supervision of Hartmut Weiß. It contains the stability and blowup-criterion results above together with background exposition in spin geometry and parabolic PDE.
Et Cetera
Lecture notes on the Ricci flow on surfaces | link
In 2019/2020 I held a class on Ricci flow on surfaces at the University of Freiburg. The notes contain short-time existence, long-time existence, and convergence on closed surfaces.