On the heat operators of cuspidally stratified Riemannian spaces (Q1095476)

The author investigates compact Riemannian spaces \(V_ n\) with the supplementary structure: a stratification of \(V_ n\) on subvarieties U is given, every vector tube \(T_ u\), defined over U, being supplied with the special stratification structure \(\pi -T_ u\to U\) and metric of \(V_ n\) satisfies certain conditions in \(T_ u\). The main result is the following: The heat operator exp(-\(\Delta\) t) on \(V_ n\) is of a trace class and there exists a constant \(K>0\), such that \[ Tr \exp (-\Delta t)\leq K\cdot t^{-n/2},\quad 0\leq t\leq t_ 0. \] Note that the proof of the main theorem is only sketched in the paper.