A note on the long neck principle and spectral width inequality of geodesic collar neighborhoods

Daoqiang Liu

doi:10.1090/proc/16869

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arXiv · 2303.15333

A note on the long neck principle and spectral width inequality of geodesic collar neighborhoods

Daoqiang Liu

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Abstract

The main purpose of this short note is to derive some generalizations of the long neck principle and give a spectral width inequality of geodesic collar neighborhoods. Our results are obtained via the spinorial Callias operator approach. An important step is to introduce the relative Gromov-Lawson pair on a compact manifold with boundary, relative to a background manifold.

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Daoqiang Liu. 2023-03-27. A note on the long neck principle and spectral width inequality of geodesic collar neighborhoods. https://doi.org/10.1090/proc%2F16869

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