2 problems

Let $M$ be an $n$-dimensional Riemannian manifold, let $c$ be a real number, and let $V_M(p,r)$ denote the volume of the geodesic ball of radius $r$ centered at $p$. Suppose that,…

Let $\mathbb{M}_{h}^{m}$ be a rotationally invariant model manifold, let $B(o,r)\subset \mathbb{M}_{h}^{m}$ be a geodesic ball, and let $\lambda_{l,i}(B(o,r))$ denote the eigenvalu…