Surfaces which contain many circles

Volume 82 / 2008

Nobuko Takeuchi Banach Center Publications 82 (2008), 201-207 MSC: 53A05, 53A30. DOI: 10.4064/bc82-0-14


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.


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

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image