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

数学物理学报 ›› 2026, Vol. 46 ›› Issue (2): 552-583.

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

敖微微(), 赖珊珊^*()

武汉大学数学与统计学院武汉 430072

收稿日期:2025-12-16 修回日期:2026-01-04 出版日期:2026-04-26 发布日期:2026-04-27
通讯作者: 赖珊珊 E-mail:wwao@whu.edu.cn;sslai_math@whu.edu.cn
作者简介:敖微微, Email：wwao@whu.edu.cn
基金资助:
国家重点研发计划(2022YFA1006800);国家自然科学基金创新研究群体项目(12221001);国家自然科学基金重点项目(12131017);国家自然科学基金面上项目(12471111)

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

Weiwei Ao(), Shanshan Lai^*()

School of Mathematics and Statistics, Wuhan University, Wuhan 430072

Received:2025-12-16 Revised:2026-01-04 Online:2026-04-26 Published:2026-04-27
Contact: Shanshan Lai E-mail:wwao@whu.edu.cn;sslai_math@whu.edu.cn
Supported by:
National Key Research and Development Program of Science and Technology(2022YFA1006800);National Natural Science Foundation of China Group Project(12221001);National Natural Science Foundation of China Key Project(12131017);National Natural Science Foundation China General Project(12471111)

摘要/Abstract

摘要：

该文旨在得到紧致 Riemann 曲面上的 $G_2$ 型 Toda 系统的完全爆破解的精确估计, 从而充分理解完全爆破解的渐近行为. 作者利用全局解的非退化性, 证明了: 1) 所有完全爆破解均可用一组具有精确误差的整体解序列逼近; 2) 特定函数的梯度在爆破点处必须以足够快的速度趋于零, 从而确定了爆破点的位置; 3) 存在对应的 $\partial_z^2$ 条件.

关键词: $G_2$ 型 Toda 系统, 完全爆破解, 渐近行为估计

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

中图分类号:

O175.23

敖微微, 赖珊珊. $G_2$ 型 Toda 系统的完全爆破解的精确估计——献给陈化教授 70 寿辰[J]. 数学物理学报, 2026, 46(2): 552-583.

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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