###### Current research

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.

###### Publications

- 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 PoincarĂ© (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.