2 papers
math.DG2024
Gap phenomena under curvature restrictions
Shouhei Honda, Andrea Mondino
In the paper we discuss gap phenomena of three different types related to Ricci (and sectional) curvature. The first type is about spectral gaps. The second type is about sharp gap…
math.DG2024
Poincaré inequality for one forms on four manifolds with bounded Ricci curvature
Shouhei Honda, Andrea Mondino
In this short note, we provide a quantitative global Poincaré inequality for one forms on a closed Riemannian four manifold, in terms of an upper bound on the diameter, a positive…