Spectral inequalities for magnetic Neumann Laplacian on rectangles

Tuyen Vu

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arXiv · 2608.03843

Spectral inequalities for magnetic Neumann Laplacian on rectangles

Tuyen Vu

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Abstract

We consider the magnetic Neumann Laplacian on rectangles, subject to non-homogeneous fields. We prove that the square is a local minimiser of the lowest eigenvalue among all rectangles of a fixed area for weak magnetic fields . We conjecture that it is a global minimiser both under the area or perimeter constraints and partially prove the conjecture by establishing lower and upper bounds to the principal eigenvalue.

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Tuyen Vu. 2026-08-04. Spectral inequalities for magnetic Neumann Laplacian on rectangles. https://arxiv.org/abs/2608.03843

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