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## Seminar on** **

**Mathematical General Relativity**

*Organizers:*

* *Philippe G. LeFloch *(Univ. Pierre et Marie Curie) *

*Ghani Zeghib (Ecole Normale Supérieure, Lyon)*

#### With the financial support of the** ****ANR Project**

#### “Mathematical General Relativity. Analysis and geometry of spacetimes with low regularity”

**Thursday Nov. 24, 2011**

### Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Paris

** Lecture room 15-25 326 (third floor)**

**Lecture room 15-25 326 (third floor)**

**14h Paul Laurain (Paris 7) Surfaces with constant mean curvature in a Riemannian manifold of dimension 3**

**Abstract. **The surfaces with constant mean curvature (CMC) in a spacelike hypersurface are geometrically and physically very interesting, as shown by Huisken and Yau in 1996 or in the beautiful thesis of Bray. However, the purpose of this talk is not to develop the physical properties of CMC surfaces but to see on an example what are the analytical difficulties encountered when studying these surfaces. In fact, we will show how to study CMC surfaces in terms of partial differential equations in order to derive geometric properties. We emphasize in particular the key difficulties generated by the conformal invariance of the problem as the phenomena of concentration and we will show how the structure of the equation helps us to overcome them.

**15h30 James D.E. Grant (Vienna) Null injectivity radius estimates**

**Abstract. **I will report on joint work with P.G. LeFloch, in which we use comparison techniques, such as the Rauch comparison theorem and Hessian comparison theorem, to estimate the null injectivity radius on a Lorentzian manifold. This work gives a more geometrical setting for work of Klainerman and Rodnianski on null injectivity radius estimates.