A Poincare inequality on loop spaces

被引：7

作者：

Chen, Xin ^{[1
]}

Li, Xue-Mei ^{[1
]}

Wu, Bo ^{[1
]}

机构：

[1] Univ Warwick, Inst Math, Coventry CV4 7AL, W Midlands, England

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2010年 / 259卷 / 06期

基金：

英国工程与自然科学研究理事会;

关键词：

Path space; Loop space; Brownian bridge measure; Poincare inequalities; Malliavin calculus; LOGARITHMIC SOBOLEV INEQUALITIES; QUASI-INVARIANCE THEOREM; PINNED BROWNIAN-MOTION; HEAT KERNEL MEASURE; MARTINGALE REPRESENTATION; DIFFERENTIAL-CALCULUS; WIENER MEASURE; SPECTRAL GAPS; INTEGRATION; PATH;

D O I：

10.1016/j.jfa.2010.05.006

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：1421 / 1442

页数：22

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