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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Convex bodies in Euclidean and Weil-Petersson geometries


Author: Sumio Yamada
Journal: Proc. Amer. Math. Soc. 142 (2014), 603-616
MSC (2010): Primary 30F60, 32G15, 58B20
Published electronically: November 13, 2013
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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.


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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
Email: yamada@math.gakushuin.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11841-1
PII: S 0002-9939(2013)11841-1
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
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.