The vanishing of \(L^2\) harmonic one-forms on based path spaces

DOI10.1016/j.jfa.2012.12.008zbMath1264.58001arXiv1204.0120OpenAlexW2084535268MaRDI QIDQ1940937

Yuxin Yang, K. David Elworthy

Publication date: 11 March 2013

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1204.0120

zbMATH Keywords

Malliavin calculusWiener measureHodge decompositionClark-Ocone formulaspectral gappath spaceBanach manifoldMarkovian connection\(L^2\) cohomology\(L^2\) harmonic forms

Mathematics Subject Classification ID

Diffusion processes and stochastic analysis on manifolds (58J65) Differential forms in global analysis (58A10) Infinite-dimensional manifolds (46T05)

Related Items (2)

De Rham–Hodge decomposition and vanishing of harmonic forms by derivation operators on the Poisson space ⋮ Weitzenböck and Clark-Ocone Decompositions for Differential Forms on the Space of Normal Martingales

Cites Work

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• Vanishing of one-dimensional \(L^2\)-cohomologies of loop groups
• Stochastic calculus with anticipating integrands
• Hodge theory with degenerating coefficients: \(L_2\) cohomology in the Poincaré metric
• The differential form spectrum of hyperbolic space
• The Lie bracket of adapted vector fields on Wiener spaces
• De Rham-Hodge-Kodaira operator on loop groups
• Analysis on loop spaces and topology
• Renormalized differential geometry on path space: Structural equation, curvature
• Introduction to differentiable manifolds.
• Random rotations of the Wiener path
• On the geometry of diffusion operators and stochastic flows
• Itô maps and analysis on path spaces
• An \(L^{2}\) theory for differential forms on path spaces. I
• Potential theory on Hilbert space
• A Weitzenböck formula for the damped Ornstein–Uhlenbeck operator in adapted differential geometry
• Generalised Clark-Ocone formulae for differential forms
• The Malliavin Calculus and Related Topics
• VANISHING THEOREM OF THE HODGE–KODAIRA OPERATOR FOR DIFFERENTIAL FORMS ON A CONVEX DOMAIN OF THE WIENER SPACE
• Geometric stochastic analysis on path spaces
• Weak Levi-Civita connection for the damped metric on the Riemannian path space and vanishing of Ricci tensor in adapted differential geometry
• An \(L^ 2\) estimate for Riemannian anticipative stochastic integrals

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