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Curvature and length

1961
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Bulletin of the American Mathematical Society
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In this note an invariance property of curvature of plane curves is discussed. The property is essentially this: the pointwise curvature of a family F of plane curves integrated over the interior of a simple, closed, smooth curve B depends only upon the angles of intersection of B with members of F. The property is exactly stated and proved below, and some of its consequences are discussed. These are first, the connection of the integrated curvature with the boundary length, and second an

doi:10.1090/s0002-9904-1961-10524-7
fatcat:ja5p7yhovfgx5f7qdz3brbh77m