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Total curvature and some characterizations of closed curves in CATk spaces

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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.

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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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Correspondence to Areeyuth Sama-Ae.

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This work is supported by Faculty of Science and Technology, Prince of Songkla University, Pattani Campus.

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Sama-Ae, A., Phon-on, A. Total curvature and some characterizations of closed curves in CATk spaces. Geom Dedicata 199, 281–290 (2019). https://doi.org/10.1007/s10711-018-0349-y

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  • DOI: https://doi.org/10.1007/s10711-018-0349-y

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