科研之友
微信
新浪微博
Facebook
分享链接
摘要
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 eigenvalue is minimal for the equilateral triangle.
- 出版日期2012-4
