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

作者：Aida Shigeki^*

来源：Journal of Functional Analysis, 2015, 269(12): 3714-3764.

DOI：10.1016/j.jfa.2015.09.023

• Spectral gap
• Loop space
• Logarithmic Sobolev inequality
• Semi-classical limit

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 et al. [13]. Further, we study the asymptotic behavior of the spectral gap.

• 出版日期2015-12-15