Spectral asymptotics for the semiclassical Bochner Laplacian of a line bundle with constant rank curvature

Léo Morin

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arXiv · 2010.00226

Spectral asymptotics for the semiclassical Bochner Laplacian of a line bundle with constant rank curvature

Léo Morin

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Abstract

The goal of this paper is manyfold. Firstly, we want to give a short introduction to the Bochner Laplacian and explain why it acts locally as a magnetic Laplacian. Secondly, given a confining magnetic field, we use Agmon-like estimates to reduce its spectral study to magnetic Laplacians, in the semiclassical limit. Finally, we use this to translate already-known spectral asymptotics for the magnetic Laplacian to the Bochner Laplacian.

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BibTeX RIS

Léo Morin. 2020-10-01. Spectral asymptotics for the semiclassical Bochner Laplacian of a line bundle with constant rank curvature. https://arxiv.org/abs/2010.00226

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