A Poincaré inequality on loop spaces
File(s)0905.3007v1.pdf (219.87 KB)
Accepted version
Author(s)
Chen, X
Li, X-M
Wu, B
Type
Journal Article
Abstract
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.
Date Issued
2010-05-26
Date Acceptance
2009-10-01
Citation
Journal of Functional Analysis, 2010, 259 (6), pp.1421-1442
ISSN
0022-1236
Publisher
Elsevier
Start Page
1421
End Page
1442
Journal / Book Title
Journal of Functional Analysis
Volume
259
Issue
6
Copyright Statement
© 2010, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/
Identifier
http://dx.doi.org/10.1016/j.jfa.2010.05.006
Subjects
Science & Technology
Physical Sciences
Mathematics
MATHEMATICS
Path space
Loop space
Brownian bridge measure
Poincare inequalities
Malliavin calculus
LOGARITHMIC SOBOLEV INEQUALITIES
COMPACT RIEMANNIAN MANIFOLD
QUASI-INVARIANCE THEOREM
PINNED BROWNIAN-MOTION
HEAT KERNEL MEASURE
WIENER MEASURE
SPECTRAL GAPS
DIFFERENTIAL-CALCULUS
PATH SPACES
INTEGRATION
math.PR
0101 Pure Mathematics
General Mathematics
Notes
mrclass: 58J65 (28C20 58B20 60H07) mrnumber: 2659766 mrreviewer: Maria Gordina
Publication Status
Published