THE LOWER SEMI-CONTINUITY OF TOTAL CURVATURE FOR CLOSED CURVES IN CAT(K ) SPACES
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
CAT(K), total curvature, lower semi-continuity, closed curve.