RESEARCH BLOG 11/24/03 I've been working on making the argument sketched in blog 11/16/03 Summary: RESEARCH BLOG 11/24/03 I've been working on making the argument sketched in blog 11/16/03 more precise. What we need to show is that for a geometrically finite end of a complete pinched negative curvature Riemannian (PNC) man- ifold M (with sectional curvature satisfying -a2 Ksec -1, a > 1), the boundary of the convex core C(M) has bounded area, only depend- ing on the pinching constants and the topological type of the boundary. This follows from the following argument of Kleiner [3]. Let Es be the points in M distance s away from C(M), so E0 = C(M). The surfaces Es are C1,1 for s > 0, so they are C2 almost everywhere, by Rademacher's theorem. Then Es GKsda 0 as s 0+ (he was taking the convex hull of a compact set, but the argument is local, so it generalizes to convex hull of limit sets), where GKs is the Gauss- Kronecker curvature of Es, the product of the principal curvatures. One can thus make sense of the equation K = Ksec + GKs at points Collections: Mathematics