Surfaces which contain many circles
Volume 82 / 2008
Banach Center Publications 82 (2008), 201-207
MSC: 53A05, 53A30.
DOI: 10.4064/bc82-0-14
Abstract
We survey the results on surfaces which contain many circles. First, we give two analyses of shapes which always look round. Then we introduce the Blum conjecture: “A closed $C^{\infty}$ surface in $E^3$ which contains seven circles through each point is a sphere”, and give some partial affirmative results toward the conjecture. Moreover, we study some surfaces which contain many circles through each point, for example, cyclides.
