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

#### Autoren: Lashi Bandara, Alan McIntosh (2016)

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.

Zeitschrift:
J. Geom. Anal.
Verlag:
Springer
Seiten:
428-462
Band:
26, no. 1

zur Übersicht der Publikationen