Canonical Euler-Lagrange equations and Jacobi's theorem on regular surfaces

In this article we establish conditions under which canonical variables can be defined for a variational problem defined on a geometric (compact) surface. Also, we show the form the corresponding Euler-Lagrange equations assume once we rewrite them in terms of such canonical variables. Furthermore,...

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Bibliographic Details
Published in:Complex variables, theory & application theory & application, 2005-11, Vol.50 (14), p.1081-1086
Main Authors: Solanilla, Leonardo, Rivera, Wilson
Format: Article
Language:English
Subjects:
AMS Mathematics Subject Classifications
Canonical variables
Conformal Gauss curvature prescription problem
Euler equation
Hamilton-Jacobi equation
Jacobi's theorem
Online Access:Get full text
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Summary:In this article we establish conditions under which canonical variables can be defined for a variational problem defined on a geometric (compact) surface. Also, we show the form the corresponding Euler-Lagrange equations assume once we rewrite them in terms of such canonical variables. Furthermore, we prove a version of Jacobi's theorem generalizing the univariate standard version of this theorem. The main results are applied to the conformal Gauss curvature functional.
ISSN:0278-1077
1563-5066
DOI:10.1080/02781070500278274