3 problems

Let $M:=M_1\times\ldots\times M_n$ be the product of at least two compact Riemannian manifolds without boundary, and let $d$ be its dimension. Denote by $N_M(\lambda)$ the eigenval…

Weyl law improvement conjecture. There exists $\delta>0$ such that

Let $M$ be an arbitrary complete connected Riemannian manifold, let $B(o,r)$ denote the geodesic ball centered at $o$, let $\mu$ be the Riemannian measure, let $G(x,o)$ be the Gree…