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arXiv · 1103.5089

The Kato Square Root Problem on Submanifolds

Andrew J. Morris
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Abstract

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 Poincaré inequality holds. This is based on the framework for Dirac type operators that was introduced by Axelsson, Keith and McIntosh.

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Andrew J. Morris. 2011-03-25. The Kato Square Root Problem on Submanifolds. https://doi.org/10.1112/jlms%2Fjds039

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