Improved spectral gap bounds on positively curved manifolds

A coupling method and an analytic one allow us to prove new lower bounds for the spectral gap of reversible diffusions on compact manifolds. Those bounds are based on the a notion of curvature of the diffusion, like the coarse Ricci curvature or the Bakry--Emery curvature-dimension inequalities. We show that when this curvature is nonnegative, its harmonic mean is a lower bound for the spectral gap