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arXiv · 2506.24059

A scalar-mean curvature comparison theorem for manifolds with iterated conical singularities

Milan Jovanovic·Jinmin Wang
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Abstract

We use the Dirac operator method to prove a scalar-mean curvature comparison theorem for spin manifolds which carry iterated conical singularities. Our approach is to study the index theory of a twisted Dirac operator on such singular manifolds. A dichotomy argument is used to prove the comparison theorem without knowing precisely the index of the twisted Dirac operator. This framework also enables us to prove a rigidity theorem of Euclidean domains and a spin positive mass theorem for asymptotically flat manifolds with iterated conical singularities.

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Milan Jovanovic, Jinmin Wang. 2025-06-30. A scalar-mean curvature comparison theorem for manifolds with iterated conical singularities. https://arxiv.org/abs/2506.24059

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