Šobr, Václav Isoperimetrische Ungleichungen für geschlossene Kurven. (On isoperimetric inequalities for closed curves). (German) Zbl 0666.52004 Čas. Pěstování Mat. 113, No. 4, 403-414 (1988). The isoperimetric inequality for plane curves is generalized to rectifiable curves in euclidean spaces \(E^ 4\), \(E^ 5\). A series of inequalities is established in which the area of the classical inequality is replaced by signed areas of projections onto 2-dimensional coordinate planes. The inequalities are proved by means of Fourier series. Reviewer: E.Heil MSC: 52A40 Inequalities and extremum problems involving convexity in convex geometry 53A04 Curves in Euclidean and related spaces 52A20 Convex sets in \(n\) dimensions (including convex hypersurfaces) Keywords:isoperimetric inequality; rectifiable curves in euclidean spaces; Fourier series PDFBibTeX XMLCite \textit{V. Šobr}, Čas. Pěstování Mat. 113, No. 4, 403--414 (1988; Zbl 0666.52004) Full Text: EuDML