Asymptotic flexibility of globally hyperbolic manifolds

In this short note, a question of patching together globally hyperbolic manifolds is adressed which appeared in the context of the construction of Hadamard states.Comment: 2 pages, submitted to 'Mathematische Zeitschrift

A note on invariant temporal functions

The purpose of this article is to present a result on the existence of Cauchy temporal functions invariant by the action of a compact group of conformal transformations in arbitrary globally hyperbolic manifolds. Moreover, the previous results about the existence of Cauchy temporal functions with additional properties on arbitrary globally hyperbolic manifolds are unified in a fully general theorem. The article is written as self-contained as possible, no prior knowledge on Lorentzian geometry is assumed.Comment: 14 pages, no figure

Applying the index theorem to non-smooth operators

We give a simple way to extend index-theoretical statements from partial differential operators with smooth coefficients to operators with coefficients of finite Sobolev order.Comment: 9 pages, no figur