A Poincare inequality on loop spaces

作者：Chen Xin; Li Xue Mei^*; Wu Bo

来源：Journal of Functional Analysis, 2010, 259(6): 1421-1442.

DOI：10.1016/j.jfa.2010.05.006

• Path space
• Loop space
• Brownian bridge measure
• Poincare inequalities
• Malliavin calculus

We show that the Laplacian on the loop space over a class of Riemannian manifolds has a spectral gap. The Laplacian is defined using the Levi-Civita connection, the Brownian bridge measure and the standard Bismut tangent spaces.

• 出版日期2010-9-15