2025/05/20 by S. Cecchini, Bernhard Hanke, Cecchini, Simone +5 · 1 citation
Mathematics · #53C23 #53C24 #53C27 #58J20 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Primary: 51F30 #Secondary: 30C65
paper · pdf · doi:10.48550/arxiv.2505.14054
openalex publication_date 2025/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
Using the index theory for twisted Dirac operators acting on sections of Lipschitz bundles over non-compact manifolds, we prove Llarull-type comparison results in scalar curvature geometry. They apply to spin Riemannian manifolds with cone-type singularities and Lipschitz comparison maps to spheres. We use the language of abstract cone operators which are introduced and studied in a general functional analytic setting and which may be of independent interest. Applying our discussion to spherical suspensions of odd-dimensional closed manifolds, we generalize a Lipschitz rigidity result of the first three named authors from even to odd dimensions. Under stronger conditions, this has already been shown by Lee-Tam using geometric flows and by Baer using an upper estimate for the smallest Dirac eigenvalue.