TY - JOUR

T1 - The Kato Square Root Problem on Vector Bundles with Generalised Bounded Geometry

AU - Bandara, Lashi

AU - McIntosh, Alan

N1 - Publisher Copyright:
© 2015, Mathematica Josephina, Inc.

PY - 2016/1/1

Y1 - 2016/1/1

N2 - 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.

AB - 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.

KW - Dirac type operators

KW - Generalised bounded geometry

KW - Holomorphic functional calculi

KW - Kato square root problem

KW - Quadratic estimates

KW - Square roots of elliptic operators

UR - http://www.scopus.com/inward/record.url?scp=84953638015&partnerID=8YFLogxK

U2 - 10.1007/s12220-015-9557-y

DO - 10.1007/s12220-015-9557-y

M3 - Article

SN - 1050-6926

VL - 26

SP - 428

EP - 462

JO - Journal of Geometric Analysis

JF - Journal of Geometric Analysis

IS - 1

ER -