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Archiv der Mathematik

, Volume 107, Issue 4, pp 423–428

First Online: 28 September 2016Received: 08 June 2016


In this little note I first recall a particularly short proof of the classical isoperimetric inequality in two dimensions. Other geometric inequalities are still open in more than two dimensions. I point out six of those.

KeywordsGeometric inequalities Cheeger set Meissner bodies Ulam floating Euler elastica Farthest point distance function This manuscript is dedicated to Ernst-Ulrich Gekeler with gratitude for his service to Archiv der Mathematik.

Mathematics Subject ClassificationPrimary 49Q10 Secondary 51M16 52A40 31C45 31B99  Download to read the full article text

Author: B. Kawohl


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