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math.DG2026
Sharp Hessian inequalities and monotonicity for Green's functions of positively curved Einstein manifolds
Cosmin Manea, Jacob Reznikov
We prove a sharp Hessian inequality for the natural comparison Green's function of an Einstein manifold with positive sectional curvature, which may be viewed as a Green's function…
math.DG2026
Sharp monotonicity for closed three-manifolds with positive scalar curvature
Cosmin Manea
We prove two sharp monotonicity formulae for the natural Green's function of a closed three-manifold with positive scalar curvature, analogous to the Munteanu-Wang theorem for non-…
math.DG2025
Sharp gradient estimates and monotonicity in positive Ricci curvature
Cosmin Manea
We prove a sharp gradient estimate for the natural Green's function of a closed manifold with positive Ricci curvature. We also show that this estimate is closely related to a fami…