731 research outputs found
The global geometry of Riemannian manifolds with commuting curvature operators
We give manifolds in both the Riemannian and in the higher signature settings
whose Riemann curvature operators commute, i.e. which satisfy
R(a,b)R(c,d)=R(c,d)R(a,b) for all tangent vectors. These manifolds have global
geometric phenomena which are quite different for higher signature manifolds
than they are for Riemannian manifolds. Our focus is on global properties;
questions of geodesic completeness and the behaviour of the exponential map are
investigated
Heat content with singular initial temperature and singular specific heat
Let (M,g) be a compact Riemannian manifold without boundary. Let D be a
compact subdomain of M with smooth boundary. We examine the heat content
asymptotics for the heat flow from D into M where both the initial temperature
and the specific heat are permitted to have controlled singularities on the
boundary of D. The operator driving the heat process is assumed to be an
operator of Laplace typ
Expected volume of intersection of Wiener sausages and heat kernel norms on compact Riemannian manifolds with boundary
Estimates are obtained for the expected volume of intersection of independent
Wiener sausages in Euclidean space in the small time limit. The asymptotic
behaviour of the weighted diagonal heat kernel norm on compact Riemannian
manifolds with smooth boundary is obtained in the small time limi
- …