Convex bodies in Euclidean and Weil-Petersson geometries
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Abstract:
A variational formulation of Funk metric defined on a convex set in a Euclidean space is introduced. The new definition provides geometric descriptions of the Finsler metric. Secondly, the variational characterization of the Funk metric is generalized to the Weil-Petersson geometry of Teichmüller spaces. Finally, a comparison between several Funk-type metrics defined on Teichmüller spaces is made.References
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Additional Information
- Sumio Yamada
- Affiliation: Mathematical Institute, Tohoku University, Aoba Sandai, 980-8578, Japan
- Address at time of publication: Department of Mathematics, Gakushuin University, Tokyo 171-8588, Japan
- MR Author ID: 641808
- Email: yamada@math.gakushuin.ac.jp
- Received by editor(s): August 22, 2011
- Received by editor(s) in revised form: March 28, 2012
- Published electronically: November 13, 2013
- Additional Notes: This work was supported in part by JSPS Grant-in-Aid for Scientific Research No. 20540201
- Communicated by: Alexander N. Dranishnikov
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 142 (2014), 603-616
- MSC (2010): Primary 30F60, 32G15, 58B20
- DOI: https://doi.org/10.1090/S0002-9939-2013-11841-1
- MathSciNet review: 3134001