Print Email Facebook Twitter The Riesz transform on a complete Riemannian manifold with Ricci curvature bounded from below Title The Riesz transform on a complete Riemannian manifold with Ricci curvature bounded from below Author Versendaal, R. Contributor van Neerven, J.M.A.M. (mentor) Faculty Electrical Engineering, Mathematics and Computer Science Department Delft Institute of Applied Mathematics Date 2016-09-08 Abstract We study the Riesz transform and Hodge-Dirac operator on a complete Riemannian manifold with Ricci curvature bounded from below. We define the Hodge-Dirac operator ∏ on Lp(ΛTM) as the closure of d + d* on smooth, compactly supported k-forms for 1 < p < ∞. Given the boundedness of the Riesz transform on Lp(ΛTM), we show that ∏ is R-bisectorial on Lp(ΛTM). From this we conclude that ∏ has a bounded H∞-functional calculus on a bisector under mild assumptions which we conjecture to be true when the Ricci curvature is nonnegative. We conclude by showing that from this bounded H∞-functional calculus for the Hodge-Dirac operator we can retrieve the boundedness of the Riesz transform, thus giving us that the mentioned assertions are equivalent when the Ricci curvature is nonnegative. Subject Riesz transformRiemannian manifoldHodge-Dirac operatorRicci curvature To reference this document use: http://resolver.tudelft.nl/uuid:878a94cc-5839-42f4-9ccf-ff48742526ef Part of collection Student theses Document type master thesis Rights (c) 2016 Versendaal, R. Files PDF MSc_thesis_Rik_Versendaal.pdf 798.71 KB Close viewer /islandora/object/uuid:878a94cc-5839-42f4-9ccf-ff48742526ef/datastream/OBJ/view