$G_2$ 型 Toda 系统的完全爆破解的精确估计——献给陈化教授 70 寿辰

Abstract

Abstract:

This paper aims to sharp estimates of fully bubbling solutions of the Toda system with Cartan matrix $G_2$ in a compact Riemann surface, thereby providing a comprehensive understanding of the asymptotic behavior of such solutions. By using the non-degeneracy results of entire solutions, it proves that: 1) All fully bubbling solutions are approximated by a sequence of global solutions with precise error estimates; 2) the gradient of certain functions must approach zero with sufficient rate at the blow-up points, which uniquely determines their locations; 3) a corresponding $\partial_z^2$ condition exists.

Key words: $G_2$ Toda system, fully bubbling solutions, asymptotic behavior

CLC Number:

O175.23

Weiwei Ao, Shanshan Lai. Sharp Estimates for Fully Bubbling Solutions of $G_2$ Toda System[J].Acta mathematica scientia,Series A, 2026, 46(2): 552-583.

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References 55

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Sharp Estimates for Fully Bubbling Solutions of $G_2$ Toda System

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