FOUR VERTICES THEOREMS FOR SURFACE CURVES AND SPACE CURVES.
Kuniho Yasunaka · Institutional Repositories DataBase (IRDB) · 1957
The so-called four vertices theorem for plane closed curves seems originally due to C. $C^{\backslash }arath\text{\'{e}} odory^{2)}$ .A. Kneser) dedicated his elegant proof to H. Weber.Thereby the vertex of an oval was the point on it, where the curvature becomes extreme.It was preceded by a paper of S. Mukhopadhyaya.1) 16) W. Blaschke $t)8)$ G. Hcrglotz, 8) H. Mohrmann, ) W. Vogt, 5) W. S\"uss 1) and D. Fog $0$ ) have given other proofs.T. Hayashi 11) has made a remark to it.P. Ganapati'7) added some theorems concerning it.