The Kato square root problem on vector bundles with generalised bounded geometry
Analysis of PDEs
2016-03-09 v4
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.
Cite
@article{arxiv.1203.0373,
title = {The Kato square root problem on vector bundles with generalised bounded geometry},
author = {Lashi Bandara and Alan McIntosh},
journal= {arXiv preprint arXiv:1203.0373},
year = {2016}
}
Comments
Slight technical modification of the notion of "GBG constant section" on page 7, and a few technical modifications to Proposition 8.4, 8.6, 8.9