A Poincaré inequality on loop spaces

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Title: A Poincaré inequality on loop spaces
Author(s): Chen, X
Li, X-M
Wu, B
Item 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.
Publication Date: 26-May-2010
Date of Acceptance: 1-Oct-2009
URI: http://hdl.handle.net/10044/1/54122
DOI: https://dx.doi.org/10.1016/j.jfa.2010.05.006
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/
Keywords: 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
math.PR
0101 Pure Mathematics
General Mathematics
Publication Status: Published
Appears in Collections:Pure Mathematics
Mathematics
Faculty of Natural Sciences



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