Neumann eigenvalue sums on triangles are (mostly) minimal for equilaterals
نویسندگان
چکیده
منابع مشابه
Neumann Eigenvalue Sums on Triangles Are (mostly) Minimal for Equilaterals
We prove that among all triangles of given diameter, the equilateral triangle minimizes the sum of the first n eigenvalues of the Neumann Laplacian, when n 3 . The result fails for n = 2 , because the second eigenvalue is known to be minimal for the degenerate acute isosceles triangle (rather than for the equilateral) while the first eigenvalue is 0 for every triangle. We show the third eigenva...
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ژورنال
عنوان ژورنال: Mathematical Inequalities & Applications
سال: 2012
ISSN: 1331-4343
DOI: 10.7153/mia-15-32