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Geodesics in Asymmetic Metric Spaces

Andrea C. G. Mennucci (2014)

Analysis and Geometry in Metric Spaces

In a recent paper [17] we studied asymmetric metric spaces; in this context we studied the length of paths, introduced the class of run-continuous paths; and noted that there are different definitions of “length spaces” (also known as “path-metric spaces” or “intrinsic spaces”). In this paper we continue the analysis of asymmetric metric spaces.We propose possible definitions of completeness and (local) compactness.We define the geodesics using as admissible paths the class of run-continuous paths.We...

Geodesics in the Heisenberg Group

Piotr Hajłasz, Scott Zimmerman (2015)

Analysis and Geometry in Metric Spaces

We provide a new and elementary proof for the structure of geodesics in the Heisenberg group Hn. The proof is based on a new isoperimetric inequality for closed curves in R2n.We also prove that the Carnot- Carathéodory metric is real analytic away from the center of the group.

Geodesies on typical convex surfaces

Peter Manfred Gruber (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Using Baire categories uniqueness of geodesic segments and existence of closed geodesics on typical convex surfaces are investigated.

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