JP Journal of Geometry and Topology
Volume 15, Issue 1, Pages 17 - 33
(February 2014)
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THE LOWER SEMI-CONTINUITY OF TOTAL CURVATURE FOR CLOSED CURVES IN CAT(K ) SPACES
A. Sama-Ae
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Abstract:
The notion of total curvature for closed curves in CAT(K) spaces is introduced. We then prove the lower semi-continuity of total curvature for closed curves in CAT(K) spaces, that is  where  is a sequence of closed curves converging to a closed curve g. In the case of that is a sequence of closed polygonal curves inscribed in g we have  |
| Keywords and phrases: CAT(K), total curvature, lower semi-continuity, closed curve. |
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