Pólya-type inequalities on spheres and hemispheres

Pedro Freitas, Jing Mao, Isabel Salavessa

Given an eigenvalue $\lambda$ of the Laplace-Beltrami operator on $n-$spheres or $-$hemispheres, with multiplicity $m$ such that $\lambda ={\lambda }_k=\cdots ={\lambda }_{k+m-1}$, we characterise the lowest a…