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arXiv · 1203.0373

The Kato square root problem on vector bundles with generalised bounded geometry

Lashi Bandara·Alan McIntosh
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Abstract

We consider smooth, complete Riemannian manifolds which are exponentially locally doubling. Under a uniform Ricci curvature bound and a uniform lower bound on injectivity radius, we prove a Kato square root estimate for certain coercive operators over the bundle of finite rank tensors. These results are obtained as a special case of similar estimates on smooth vector bundles satisfying a criterion which we call generalised bounded geometry. We prove this by establishing quadratic estimates for perturbations of Dirac type operators on such bundles under an appropriate set of assumptions.

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Lashi Bandara, Alan McIntosh. 2012-03-02. The Kato square root problem on vector bundles with generalised bounded geometry. https://doi.org/10.1007/s12220-015-9557-y

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