Abstract cone operators and Lipschitz rigidity for scalar curvature on singular manifolds

Simone Cecchini; Bernhard Hanke; Thomas Schick; Lukas Schoenlinner

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arXiv · 2505.14054

Abstract cone operators and Lipschitz rigidity for scalar curvature on singular manifolds

Simone Cecchini·Bernhard Hanke·Thomas Schick·Lukas Schoenlinner

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Abstract

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.

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BibTeX RIS

Simone Cecchini, Bernhard Hanke, Thomas Schick, Lukas Schoenlinner. 2025-06-18. Abstract cone operators and Lipschitz rigidity for scalar curvature on singular manifolds. https://arxiv.org/abs/2505.14054

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