4 problems

Let $P$ be a Laplace type operator in dimension $d$ with principal symbol … where $g^{\mu\nu}$ is the metric and $u$ is a positive invertible matrix. A heat-trace coefficient $a_r$…

Let $\mathcal{M}$ be modeled on an irreducible simply connected symmetric space $G/K$ of non-compact type. Let $\mathcal{A}_n(\mathcal{M})$ denote its heat trace coefficients, and…

Let $B$ be a ball in $mathbb{R}^m$, and let $beta$ denote the parameter in the heat-trace coefficient asymptotic … Here $ell(B)$ is the length of the shortest accessible periodi…

Let $Omega$ be a planar domain, let $ell(Omega)$ denote the length of its shortest accessible periodic geodesic, and suppose the heat-trace coefficient has the asymptotic form ……