The smooth Riemannian extension problem: completeness
Differential Geometry
2016-07-01 v2 Metric Geometry
Abstract
By means of a general gluing and conformal-deformation construction, we prove that any smooth, metrically complete Riemannian manifold with smooth boundary can be realized as a closed domain into a smooth, geodesically complete Riemannan manifold without boundary. Applications to Sobolev spaces, Nash embedding and local extensions with strict curvature bounds are presented.
Cite
@article{arxiv.1601.05075,
title = {The smooth Riemannian extension problem: completeness},
author = {Stefano Pigola and Giona Veronelli},
journal= {arXiv preprint arXiv:1601.05075},
year = {2016}
}
Comments
This paper has been included in arXiv:1606.08320 where we also consider the Riemannian extension problem under a control of the sectional and the Ricci curvatures