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 -