The Kato Square Root Problem on Submanifolds

Details The Kato Square Root Problem on Submanifolds The Kato Square Root Problem on Submanifolds

2011-03-25

arxiv.org/abs/1103.5089v1

Mathematics

Analysis of PDEs

34 pages

Scientific paper

We solve the Kato square root problem for divergence form operators on complete Riemannian manifolds that are embedded in Euclidean space with a bounded second fundamental form. We do this by proving local quadratic estimates for perturbations of certain first-order differential operators that act on the trivial bundle over a complete Riemannian manifold with at most exponential volume growth and on which a local Poincar\'{e} inequality holds. This is based on the framework for Dirac type operators that was introduced by Axelsson, Keith and McIntosh.

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