A well known isoperimetric inequality for closed curves in $ \mathbb{R}^2$ can be generalized to closed curves in $ \mathbb{R}^{2n}$ , see: https://mathoverflow.net/a/321505/121665. I have two questions: Question 1. Is it possible to prove a reasonable isoperimetric inquality for closed curves in $ \mathbb{R}^{2n+1}$ ? Questions 2. Can an inequality from https://mathoverflow.net/a/321505/121665 be generalized toRead more