Total curvature and some characterizations of closed curves in CATk spaces
- 33 Downloads
In this paper, we study the characterizations of a closed curve in a CAT(k) space that bounds a geodesic surface which is isometric to the disk bounded by a circle in the model space \(S_k\) with same perimeter.
KeywordsCAT(k) Total curvature Closed curve
Mathematics Subject Classification (2000)51K99
The authors would like to thank referees for comments and suggestions, which are very helpful to improve the manuscript. This work is supported by Faculty of Science and Technology, Prince of Songkla University, Pattani Campus, Pattani 94000, Thailand.
- 4.Alexandrov, A.D.: Theory of curves based on the approximation by polygonal lines, Nautch. sess. Leningr. Univer., Tesis dokl. na sekth. matem. nauk. (1946)Google Scholar
- 16.Reshetnyak, Y.G.: Nonexpanding maps in a space of curvature no greater than \(K\). Sibirskii Mat. Zh. 9, 918–928 (1968)Google Scholar