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arXiv · 2410.09809

The odd-dimensional long neck problem via spectral flow

Pengshuai Shi
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Abstract

In this paper, we establish a scalar-mean curvature comparison theorem for the long neck problem on odd-dimensional spin manifolds. This extends previous work of Cecchini and Zeidler, and gives a complete answer to Gromov's long neck problem in terms of spin manifolds. As a related question, we prove a quantitative version of Llarull's theorem on non-compact spin manifolds. Our results are derived by studying the spectral flow of a family of Callias operators.

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Pengshuai Shi. 2024-10-13. The odd-dimensional long neck problem via spectral flow. https://doi.org/10.1093/imrn%2Frnaf262

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