L^p-Analysis of the Hodge--Dirac operator associated with Witten Laplacians on complete Riemannian manifolds

2017/02/20 by Jan van Neerven, van Neerven, Jan, Rik Versendaal +1 · 1 citation
Mathematics · #58J35 #58J60 #Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations #Primary: 47A60 #Secondary: 58A10 #math.DG #math.FA #msc:47A60 #msc:58A10 #msc:58J35 #msc:58J60

paper · pdf · doi:10.48550/arxiv.1702.05886

23 pages, submitted for publication

arxiv created 2017/02/20 · openalex publication_date 2017/02/20 · arxiv updated 2017/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove R-bisectoriality and boundedness of the H^∞-functional calculus in L^p for all 1<p<∞ for the Hodge-Dirac operator associated with Witten Laplacians on complete Riemannian manifolds with non-negative Bakry-Emery Ricci curvature on k-forms.

Citations

• On the parabolic kernel of the Schrödinger operator

Cited by

• Weak (1,1) Boundedness of Riesz Transforms on Vector Bundles

Related

• Holomorphic functional calculus of Hodge-Dirac operators in Lp
• Remarks on functional calculus for perturbed first order Dirac operators
• The L^p-index of the Hodge-Dirac operator on compact Riemannian manifolds
• L^p-spectrum of the Dirac operator on products with hyperbolic spaces
• Curvature, Dolbeault-Dirac operators, and an L^p-index theorem on compact Kähler manifolds