Regularized Trace of the Perturbed Laplace–Beltrami Operator on Two-Dimensional Manifolds with Closed Geodesics

The main result of the paper is the determination of the regularized trace of the Laplace–Beltrami operator with potential on the manifold given by a function family of smooth almost Liouville metrics on the sphere (besides, all the geodesics of these metrics are closed and have equal length).