Currently, I’m working with ‘nice’ foliations of asymptotically Euclidean or asymptotically hyperbolic Riemannian (or Lorentzian) manifolds and study for example their evolution in time (under Einstein’s equations). For example, I use the unique foliation by stable spheres of constant mean curvature introduced by Huisken-Yau in 1996.
- Nerz, Geometric characterizations of asymptotically hyperbolic Riemannian 3-manifolds by the existence of a suitable CMC-foliation [preprint (2017)]
- Nerz, Existence and uniqueness of constant mean curvature foliations of general asymptotically hyperbolic 3-manifolds [preprint (2016)]
- Nerz, Foliations by spheres with constant expansion for isolated systems without asymptotic symmetry [preprint (2015) (accepted by JDG)]
- Nerz, Geometric characterizations of asymptotic flatness and linear momentum in general relativity [J. Funct. Ana. (2015), preprint (2014)]
- Nerz, Foliations by stable spheres with constant mean curvature for isolated systems without asymptotic symmetry [Cal. of Var. and PDE’s (2015), preprint (2014)]
- Cederbaum, Nerz, Explicit Riemannian manifolds with unexpectedly behaving center of mass [Ann. Henri Poincaré (2014), preprint (2013)]
- Nerz, Time evolution of ADM and CMC center of mass in general relativity [preprint (2013)]
Remark on arXiv
There are several reasons why I link to the arXiv files even for the articles accepted in a journal. The two most important ones are:
- Not everybody has access to all these journals. As a researcher paid by the public, I feel that it would be incorrect if ‘the public’ could not access all of my finished research.
- It is quite hard to update articles which are already published in journals, but sometimes you find minor mistakes or want to clearify something in an articles you published. I do this by changing the arXiv version of the paper. Thus, I recommend to everybody to read the arXiv version of my papers and not the journal version. Note that due to legal issues, I can sometimes not update some of the arXiv files in the first year after it was published in a journal.