  By comparing the Laplace spectrum of the sphere $\mathbb{S}^n$ to its Weyl
function $w(x) = \frac{\omega_n}{(2\pi)^n}|\mathbb{S}^n|x^{n/2}$, we show that
no analogue of P\'olya's eigenvalue conjecture holds in general for Riemannian
manifolds with positive sectional curvature.

Differential Geometry;Spectral Theory