Comparison of the first positive Neumann eigenvalues for rectangles and special parallelograms
Metric Geometry
2018-10-17 v1 Spectral Theory
Abstract
First non-zero Neumann eigenvalues of a rectangle and a parallelogram with the same base and area are compared in case when the height of the parallelogram is greater than the base. This result is applied to compare first non-zero Neumann eigenvalue normalized by the square of the perimeter on the parallelograms with a geometrical restriction and the square. The result is inspired by Wallace--Bolyai--Gerwien theorem. An interesting three-dimensional problem related to this theorem is proposed.
Keywords
Cite
@article{arxiv.1810.07025,
title = {Comparison of the first positive Neumann eigenvalues for rectangles and special parallelograms},
author = {Arseny Raiko},
journal= {arXiv preprint arXiv:1810.07025},
year = {2018}
}