Asian Journal of Mathematics

Volume 23 (2019)

Number 6

Outermost apparent horizons diffeomorphic to unit normal bundles

Pages: 1013 – 1040

DOI: https://dx.doi.org/10.4310/AJM.2019.v23.n6.a8

Authors

Mattias Dahl (Institutionen för Matematik, Kungliga Tekniska Högskolan, Stockholm, Sweden)

Eric Larsson (Institutionen för Matematik, Kungliga Tekniska Högskolan, Stockholm, Sweden)

Abstract

Given a submanifold $S \subset \mathbb{R}^n$ of codimension at least three, we construct an asymptotically Euclidean Riemannian metric on $\mathbb{R}^n$ with nonnegative scalar curvature for which the outermost apparent horizon is diffeomorphic to the unit normal bundle of $S$.

Keywords

asymptotically Euclidean manifolds, nonnegative scalar curvature, outermost apparent horizons

2010 Mathematics Subject Classification

Primary 53C21. Secondary 53A10, 53C80, 83C57.

Received 24 January 2018

Accepted 16 November 2018

Published 3 August 2020