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Isoperimetrische Ungleichungen für geschlossene Kurven. (On isoperimetric inequalities for closed curves). (German) Zbl 0666.52004

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)
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