# Publishing house / Banach Center Publications / All volumes

## 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.

#### Authors

• Nobuko TakeuchiDepartment of Mathematics
Tokyo Gakugei University
Koganei-shi, Tokyo, 184-8501, Japan
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