ABSTRACT
In Chapter 2, we discuss the heat content asymptotics. We adopt the following notational conventions throughout. Let M be a compact Riemannian manifold of dimension m with smooth boundary ∂M. Let V be a smooth vector bundle over M and let D be an operator of Laplace type on C∞(V).Let D B be the realization of D with respect to the boundary conditions defined by a suitable boundary operator B. We shall always assume that (D,B) is elliptic with respect to a cone Cδ for https://www.w3.org/1998/Math/MathML"> 0 ≤ δ < π 2 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429208423/53d5c7c8-829c-46bf-80e4-a63fb84682ce/content/eq1.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> ; we refer to the discussion in Sections 1.4 and 1.5 for further details. Let D B be the associated realization.
