On the linear isoperimetric inequality
The author proves the following estimate for the area A(X) of a minimal surface X parametrized over the unit disc B in \({\mathbb{R}}^ 2: A(X)\leq R L(X| \partial B)\) where R is the radius of the smallest ball containing X(B) and L(X\(| \partial B)\) denotes the length of the boundary curve. This inequality being true for surfaces in \({\mathbb{R}}^ N\), the equality sign is only discussed for \(N=3:\) equality holds if and only if X is a plane disc of radius R. Two applications to minimal surfaces with free boundaries are given.
scientific article; zbMATH DE number 3915130