This paper considers some fundamental questions concerning marginally trapped surfaces, or apparent horizons, in Cauchy data sets for the Einstein equation. An area estimate for outermost marginally trapped surfaces is proved. The proof makes use of an existence result for marginal surfaces, in the presence of barriers, curvature estimates, together with a novel surgery construction for margina...

introduction: marginal adaptation of cast restorations is essential for their long-term success. as dentists usually assign ditching of dies to laboratory technicians, and ditching has a significant effect on marginal adaptation, the aim of this study was to compare ditching by laboratory technicians and standard approach on marginal adaptation of cast restoration. materials and methods: in thi...