3 problems

Let $M$ be a sufficiently smooth unknown manifold, and consider spectrum estimation for a weighted Laplace operator on $M$. Unknown-manifold rate conjecture. Lack of direct access…

Let $M$ be a smooth manifold with metric $g$, and let $\hat M$ be an estimated manifold with metric $\hat g$. Weighted-Laplacian stability conjecture. Crude stability results for t…

Let $G/H$ be a reductive symmetric space, let $X=G/H$, and let $\Gamma$ be a discrete subgroup of $G$ acting properly discontinuously and freely on $X$. Writing…