TY - JOUR
T1 - Density problems on vector bundles and manifolds
AU - Bandara, Lashi
N1 - Publisher Copyright:
© 2014, American Mathematical Society.
PY - 2014/8/1
Y1 - 2014/8/1
N2 - We study some canonical differential operators on vector bundles over smooth, complete Riemannian manifolds. Under very general assumptions, we show that smooth, compactly supported sections are dense in the domains of these operators. Furthermore, we show that smooth, compactly supported functions are dense in second order Sobolev spaces on such manifolds under the sole additional assumption that the Ricci curvature is uniformly bounded from below.
AB - We study some canonical differential operators on vector bundles over smooth, complete Riemannian manifolds. Under very general assumptions, we show that smooth, compactly supported sections are dense in the domains of these operators. Furthermore, we show that smooth, compactly supported functions are dense in second order Sobolev spaces on such manifolds under the sole additional assumption that the Ricci curvature is uniformly bounded from below.
KW - Density problems
KW - First order operators on vector bundles
KW - Laplacian on vector bundles
KW - Second order Sobolev spaces on manifolds
UR - http://www.scopus.com/inward/record.url?scp=84924785869&partnerID=8YFLogxK
U2 - 10.1090/S0002-9939-2014-12284-2
DO - 10.1090/S0002-9939-2014-12284-2
M3 - Article
SN - 0002-9939
VL - 142
SP - 2683
EP - 2695
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 8
ER -