Spectrum of 2-dimensional manifolds
Alois Švec · Czechoslovak Mathematical Journal · 1988
I get results in the following two directions: (i) It is well known, see [2], that the interval (-oo, 2 min M K) does not belong to Spec 1 (M 2 ), K being the Gauss curvature.Here, I prove that even (2 max M K, 6 min M К) ф Spec 1 (M 2 ).To accomplish this, I study the more general equation (A + /) œ = 0 ofthe Schrödinger type with /: M 2 ^ R a function; compare with [l].(ii) According to [3], the eigenvalues of A on Д 1 ^2), S 2 = S 2 (1) a unit sphere, are 1 A k = (fc + 1) (k + 2); k = 0, 1, 2,... , and the multiplicity of x X k is 2(2fc + 3)/(fc + 1).I get the multiplicity of 1 Я 1 = 6 equal to 10 in contradiction to the just quoted formula.