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

 

Finsler metrics and action potentials


Authors: Renato Iturriaga and Héctor Sánchez-Morgado
Journal: Proc. Amer. Math. Soc. 128 (2000), 3311-3316
MSC (2000): Primary 37J50, 70H30
Published electronically: April 28, 2000
MathSciNet review: 1777579
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Abstract:

We study the behavior of Mañé's action potential $\Phi_k$ associated to a convex superlinear Lagrangian, for $k$ bigger than the critical value $c(L)$. We obtain growth estimates for the action potential as a function of $k$. We also prove that the action potential can be written as $\Phi_k(x,y)=D_F(x,y)+f(y)-f(x)$ where $f$ is a smooth function and $D_F$ is the distance function associated to a Finsler metric.


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Additional Information

Renato Iturriaga
Affiliation: CIMAT, A.P. 402, 36000, Guanajuato. Gto., México
Email: renato@fractal.cimat.mx

Héctor Sánchez-Morgado
Affiliation: Instituto de Matemáticas, UNAM, Ciudad Universitaria, C. P. 04510, México, DF, México
Email: hector@matem.unam.mx

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05710-5
PII: S 0002-9939(00)05710-5
Received by editor(s): December 28, 1998
Published electronically: April 28, 2000
Additional Notes: Both authors were partially supported by CONACYT-México grant # 28489-E
Communicated by: Michael Handel
Article copyright: © Copyright 2000 American Mathematical Society