The odd-dimensional long neck problem via spectral flow

2024/10/13 by Pengshuai Shi, Shi, Pengshuai · 1 citation
Mathematics · Physics and Astronomy · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2410.09809

openalex publication_date 2024/10/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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