The relative volume growth of minimal submanifolds
Let \(P^m\) be a minimal submanifold of a Riemannian manifold \(N^n\) with sectional curvatures \(K_N\) satisfying \(K_N\leq b\). Let \(D_r\) be the connected component of the intersection of \(P\) with a ball of radius \(r\) in \(N\) with center \(p\) in \(P\), with \(r\) small. Then \(D_r\) is an \(m\)-dimensional ball. This paper compares the volume of \(D_r\) with the volume of a ball of radius \(r\) in an \(m\)-dimensional space form of constant curvature \(b\).
scientific article; zbMATH DE number 1889280