Sharp isoperimetric inequalities and sphere theorems
Sharp isoperimetric inequalities and sphere theorems
Various relations between sharp isoperimetric inequalities and volumes of manifolds are studied.In particular, we introduce and estimate sharp isoperimetric constants τ * and γ * corresponding to two types of isoperimetric inequalities.We show that for a complete n-dimensional manifold M with Ricci curvature Ric(M) ≥ n -1, the volume of …