Analytic Aspects of the Toda system: I. A Moser-Trudinger inequality

revised version: November 2000
Jürgen Jost, and Guofang Wang
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Submission date: 10. Dec. 2000
Pages: 33
published in: Communications on pure and applied mathematics, 54 (2001) 11, p. 1289-1319 
DOI number (of the published article): 10.1002/cpa.10004
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Abstract:
In this paper, we analyze solutions of the open Toda system and establish an optimal Moser-Trudinger type inequality for this system. Let be a closed surface with area 1 and the Cartan matrix for SU(N+1), i.e.,

We show that

has a lower bound in if and only if

has a lower bound in if and only if As a direct consequence, if for , has a minimizer u which satisfies