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

Bandara, Lashi; McIntosh, Alan


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...[Show more]

CollectionsANU Research Publications
Date published: 2015-01-27
Type: Journal article
Source: The Journal of Geometric Analysis
DOI: 10.1007/s12220-015-9557-y


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