Upper Bounds for the First Eigenvalue of the Laplace-Beltrami Operator Michael Gage Indiana University Mathematics Journal 1980 text pdf 10.1512/iumj.1980.29.29061 10.1512/iumj.1980.29.29061 en Indiana Univ. Math. J. 29 (1980) 897 - 912 state-of-the-art mathematics http://iumj.org/access/