Total curvature and some characterizations of closed curves in CATk spaces

Original Paper
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Abstract

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.

Keywords

CAT(kTotal curvature Closed curve 

Mathematics Subject Classification (2000)

51K99 

Notes

Acknowledgements

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.

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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics and Computer Sciences, Faculty of Science and TechnologyPrince of Songkla UniversityMuangThailand

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