Given an algebraic surface $S$ defined by an algebraic equation such
as $x^{4}+2y^{4}+3z^{4}=1$, how would one find the third smallest
eigenvalue $\mu_{3}$ for the differential equation $\Delta f\left(x,y,z\right)=-\mu_{3}f\left(x,y,z\right)$
in the region enclosed by $S$ with $f$ vanishes on $S$? Thanks.