The Generalized Legendre transform and its applications to inverse spectral problems

Victor Guillemin, Zuoqin Wang

Let $M$ be a Riemannian manifold, $\tau :G\times M\to M$ an isometric action on $M$ of an $n$-torus $G$ and $V:M\to \mathbb{R}$ a bounded $G$-invariant smooth function. By $G$-inva…