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arXiv · 1601.05075

The smooth Riemannian extension problem: completeness

Stefano Pigola·Giona Veronelli
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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.

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Stefano Pigola, Giona Veronelli. 2016-06-30. The smooth Riemannian extension problem: completeness. https://arxiv.org/abs/1601.05075

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