The Log-Sobolev Inequality on Loop Space over a Compact Riemannian Manifold
✍ Scribed by Fu-Zhou Gong; Zhi-Ming Ma
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 371 KB
- Volume
- 157
- Category
- Article
- ISSN
- 0022-1236
No coin nor oath required. For personal study only.
✦ Synopsis
We obtain a log-Sobolev inequality with a neat and explicit potential for the gradient on a based loop space over a compact Riemannian manifold. The potential term relies only on the curvature of the manifold and the Hessian of the heat kernel, and is L p -integrable for all p 1. The log-Sobolev inequality is derived by a martingale representation theorem for the differentiable functions on loop space, which is a variation of the Clark Ocone Haussmann formula.
1998 Academic Press conditional expectation of certain Wiener functionals. For details see . Using methods different from , in the present paper we also extend Gross's result to based loop space over a compact Riemannian manifold. We establish a log-Sobolev inequality with an added potential which depends article no.