Friedlander's inequality and the de Rham complex
Abstract
Inequalities between Dirichlet and Neumann eigenvalues of the Laplacian and of other differential operators have been intensively studied in the past decades. The aim of this paper is to introduce differential forms and the de Rham complex in the study of such inequalities. We show how differential forms lie hidden at the heart of the work of Rohleder on inequalities between Dirichlet and Neumann eigenvalues for the Laplacian on planar domains.
Keywords
Cite
@article{arxiv.2412.03369,
title = {Friedlander's inequality and the de Rham complex},
author = {Magnus Fries and Magnus Goffeng and Germán Miranda},
journal= {arXiv preprint arXiv:2412.03369},
year = {2026}
}
Comments
Version 1: 15 pages. Version 2: Updated version with new title and erroneous claims in Section 4 removed. 14 pages. Additional reference in Section 1 added. Version 3: 14 pages. Updated version with correct title and an additional reference. Version 4: Updated version with new title and erroneous claims in Section 4 removed