Title: Isoperimetric inequalities for eigenvalues of triangles

Authors: Bartlomiej Siudeja

Issue: Volume 59 (2010), Issue 3, 1097-1120

Abstract: Isoperimetric lower bounds for the first eigenvalue for the Dirichlet Laplacian on arbitrary triangles are proved using various symmetrization techniques. It is also shown that among triangles, the equilateral triangle maximizes the spectral gap and (under additional assumption) the ratio of the first two eigenvalues.