3,483 research outputs found
Existence and Non-existence of Half-Geodesics on
In this paper we study half-geodesics, those closed geodesics that minimize
on any subinterval of length . For each nonnegative integer ,
we construct Riemannian manifolds diffeomorphic to admitting exactly
half-geodesics. Additionally, we construct a sequence of Riemannian manifolds,
each of which is diffeomorphic to and admits no half-geodesics, yet which
converge in the Gromov-Hausdorff sense to a limit space with infinitely many
half-geodesics.Comment: This version has been shortened for publicatio
Characterizing Round Spheres Using Half-Geodesics
A half-geodesic is a closed geodesic realizing the distance between any pair
of its points. All geodesics in a round sphere are half-geodesics. Conversely,
this note establishes that Riemannian spheres with all geodesics closed and
sufficiently many half-geodesics are round
An Economic Model of Fair Use
The doctrine of fair use allows limited copying of creative works based on the rationale that copyright holders would consent to such uses if bargaining were possible. This paper develops a formal model of fair use in an effort to derive the efficient legal standard for applying the doctrine. The model interprets copies and originals as differentiated products and defines fair use as a threshold separating permissible copying from infringement. The analysis highlights the role of technology in shaping the efficient standard. Discussion of several key cases illustrates the applicability of the model.Fair use, Copyright law, Technological improvement
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