Asymptotics of spectral gaps on loop spaces over a class of Riemannian manifolds

Abstract

We prove the existence of spectral gaps of Ornstein-Uhlenbeck operators on loop spaces over a class of Riemannian manifolds which include hyperbolic spaces. This is an alternative proof and an extension of a result in Chen-Li-Wu in J. Funct. Anal. 259 (2010), 1421-1442. Further, we study the asymptotic behavior of the spectral gap.

This paper contains the subject in arXiv:1110.2307. This version is accepted for publication in Journal of Functional Analysis

References in corpus (4)

• Vanishing of one dimensional L^2-cohomologies of loop groups
• A Poincaré Inequality on Loop Spaces
• Path Integrals on a Compact Manifold with Non-negative Curvature
• Large deviation principle of Freidlin-Wentzell type for pinned diffusion processes