Isoperimetric inequalities for eigenvalues of triangles Bartlomiej Siudeja 35P15eigenvaluessymmetrizationpolarizationvariational methodspolynomial inequalities 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. Indiana University Mathematics Journal 2010 text pdf 10.1512/iumj.2010.59.3744 10.1512/iumj.2010.59.3744 en Indiana Univ. Math. J. 59 (2010) 1097 - 1120 state-of-the-art mathematics http://iumj.org/access/