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Complete 3-manifolds of positive scalar curvature with quadratic decay
Florent Balacheff, Teo Gil Moreno de Mora Sardà, Stéphane Sabourau
We prove that if an orientable 3-manifold admits a complete Riemannian metric whose scalar curvature is positive and has a subquadratic decay at infinity, then it decomposes as…
Diastolic and isoperimetric inequalities on surfaces
Florent Balacheff, Stéphane Sabourau
We prove a universal inequality between the diastole, defined using a minimax process on the one-cycle space, and the area of closed Riemannian surfaces. Roughly speaking, we show…
A Basmajian-type inequality for Riemannian surfaces
Florent Balacheff, David Fisac
We explore for compact Riemannian surfaces whose boundary consists of a single closed geodesic the relationship between orthospectrum and boundary length. More precisely, we establ…