Published on *Max Planck Institute for Mathematics* (http://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

Qiyu Chen
Affiliation:

Sun Yat-sen University/ MPIM
Date:

Thu, 2018-05-03 16:30 - 17:30 Constant mean curvature (CMC) and constant sectional curvature hypersurfaces in $n$-dimensional ($n\geq 3$) Lorentzian manifolds (also called spacetimes) play an important role in pseudo-Riemannian geometry and general relativity.

Here we focus on the 3-dimensional case. It was shown by Barbot, B$\acute{e}$guin and Zeghib that every 3-dimensional GHMC (globally hyperbolic maximal compact) Minkowski spacetime admits a unique CMC foliation and a unique CGC (constant Gauss curvature) foliation.

In this talk, we are interested in the singular case, that is, 3-dimensional convex GHM Minkowski spacetimes with particles (cone singularities of angles less than $\pi$ along time-like curves), which are used in the physics literature to model point particles in 3d gravity. We will show that the corresponding results still hold in the singular case, using a method different from the regular case and some tools of Teichmüller theory with cone singularities. This is joint work with Andrea Tamburelli.

**Links:**

[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] http://www.mpim-bonn.mpg.de/node/3444

[3] http://www.mpim-bonn.mpg.de/node/4652