5 problems

Let $M^n$ be a closed Riemannian manifold satisfying … Here $C_{P,k}$ denotes the Poincaré constant for $k$-forms. Sectional-curvature spectral gap conjecture. For every $k\ge 1$,…

Let $M^n$ be a closed Riemannian manifold with … Here $C_{P,1}$ denotes the Poincaré constant for $1$-forms. Honda–Mondino's spectral gap conjecture. Under these assumptions, … Thi…

Kannan–Lovász–Simonovits conjecture. There is a universal constant $C>0$ such that

Exponential-concentration Poincaré conjecture. There exists a constant $C(M)$ such that

Weighted orthogonality Poincaré conjecture. One has