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Comparison of the first positive Neumann eigenvalues for rectangles and special parallelograms. (arXiv:1810.07025v1 [math.MG])
来源于:arXiv
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. 查看全文>>
