Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2000-11-20
J.Geom.Phys. 41 (2002) 1-12
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Latex2e, 13 pages in A4 format
Scientific paper
We study fine differentiability properties of horizons. We show that the set of end points of generators of a n-dimensional horizon H (which is included in a (n+1)-dimensional space-time M) has vanishing n-dimensional Hausdorff measure. This is proved by showing that the set of end points of generators at which the horizon is differentiable has the same property. For 1\le k\le n+1 we show (using deep results of Alberti) that the set of points where the convex hull of the set of generators leaving the horizon has dimension k is ``almost a C^2 manifold of dimension n+1-k'': it can be covered, up to a set of vanishing (n+1-k)-dimensional Hausdorff measure, by a countable number of C^2 manifolds. We use our Lorentzian geometry results to derive information about the fine differentiability properties of the distance function and the structure of cut loci in Riemannian geometry.
Chrusciel Piotr T.
Fu Joseph H. G.
Galloway Gregory J.
Howard Ralph
No associations
LandOfFree
On fine differentiability properties of horizons and applications to Riemannian geometry does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On fine differentiability properties of horizons and applications to Riemannian geometry, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On fine differentiability properties of horizons and applications to Riemannian geometry will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-573599