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The Kato Square Root Problem on Submanifolds

By Andrew J. Morris


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.Comment: 34 page

Topics: Mathematics - Analysis of PDEs, 58J05, 47B44, 47F05
Year: 2011
DOI identifier: 10.1112/jlms/jds039
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