[CvGmt News] Seminario Analisi - Geometria

[Carlo Mantegazza]

Nell'ambito del seminario sui ``Flussi di Metriche'' il Prof.
Lars Andersson (Royal Institute of Technology - Stockoholm)
terra' due seminari nei giorni 9/1/2001 e 11/1/2001 alle ore
16.00, in Sala dei Seminari del DipMat di Pisa, dal titolo

"Constant Mean Curvature Foliations of Space-Times, the Yamabe
Invariant and the Sigma-constant"

TUtti gli interessati sono invitati,

--------------------------------------------------------------------------

9/1/2001 - Constant mean curvature foliations of flat space--times

Abstract: We prove that every maximal globally hyperbolic flat space-time
of dimension n+1, n\geq 2, with compact Cauchy surface M of hyperbolic
type, is globally foliated by constant mean curvature hypersurfaces. The
rescaled Hamiltonian  H = | \tr K|^n Vol(M) is monotone decreasing for n
\geq 3, and satisfies H \geq n^n Vol(M,g_0) where g_0 is the hyperbolic
metric on M.
The results presented generalize earlier results on 2+1 gravity from the
ADM point of view.


11/1/2001 - The singularity of flat space-times

Abstract: I will give a characterization of the limiting behavior of
constant mean curvature hypersurfaces in the direction of the singularity,
for a limited class of flat space-times of dimension n+1, n\geq 2. In the
case of 2+1 gravity I will discuss the blowup of the Dirichlet energy at
the singularity.

--------------------------------------------------------------------------