5 problems

Quantitative maximal local rewinding volume rigidity conjecture. There exists $\epsilon(n,\rho)>0$ such that, for every $0<\epsilon<\epsilon(n,\rho)$, these assumptions imply that…

Conjecture on convex level sets in Alexandrov spaces. The level set $\{f=c\}$ is an Alexandrov space of curvature at least $\kappa$.

Let $(N^n,g)$ be a complete Riemannian manifold with nonempty boundary, equipped with a smooth function $f$. Suppose that $N$ has nonnegative $m$-Bakry–Émery Ricci curvature and th…

Let $M$ be a Riemannian manifold of nonnegative variable curvature, let $\{x_i\}_{i=1}^N\subset M$, and let $w_i$ be weights used to form the geodesic convex combination from a poi…

Let $(\Sigma,g,N)$ be a complete solution of the Static Einstein equations with regular but possibly disconnected (non-empty) horizon $\partial\Sigma$. Suppose that the conformal m…