The smooth Riemannian extension problem: completeness

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.

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

References in corpus (1)

• A note on scalar curvature and the convexity of boundaries

Cited by in corpus (1)

• $L^p$-$L^q$ boundedness of pseudo-differential operators on smooth manifolds and its applications to nonlinear equations