三维拓展里奇孤立子的体积增长

三维拓展里奇孤立子的体积增长

Volume Growth for Gradient Steady Solitons of the Extended Ricci Flow

摘要/Abstract

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数学物理学报 ›› 2025, Vol. 45 ›› Issue (3): 850-857.

陈驰洲(),郭洪欣^*()

温州大学数理学院浙江温州 325035

收稿日期:2024-07-15 修回日期:2025-01-13 出版日期:2025-06-26 发布日期:2025-06-20
通讯作者: *郭洪欣, Email: guo@wzu.edu.cn
作者简介:陈驰洲, Email: chencz20000224@163.com
基金资助:
浙江省自然科学基金(LY22A010007)

Chen Chizhou(),Guo Hongxin^*()

School of Mathematics and Physics, Wenzhou University, Zhejiang Wenzhou 325035

Received:2024-07-15 Revised:2025-01-13 Online:2025-06-26 Published:2025-06-20
Supported by:
Zhejiang Provincial Natural Science Foundation of China(LY22A010007)

摘要：

该文研究 3 维拓展里奇流中完备、非紧的稳定梯度孤立子, 证明了在一定的假设条件下, 势函数的等值面的平均曲率关于距离函数是不超过线性增长的. 在此基础上, 证明了它的等值面的面积是不超过线性增长的、次等值集的体积是不超过平方增长的.

关键词: 拓展里奇流, 梯度孤立子, 体积增长

Abstract:

In this paper, we derive an estimate on the level surface of the potential function of the complete noncompact gradient steady soliton of extended Ricci flow. We show that the average curvature of the level surface of the potential function grows at most linearly with respect to the distance function under certain conditions. Based on that, we prove that the area of the level surface grows at most linearly and the volume of the sublevel sets grows at most quadratically.

Key words: extended Ricci flow, gradient soliton, volume growth

中图分类号:

O186.12

陈驰洲, 郭洪欣. 三维拓展里奇孤立子的体积增长[J]. 数学物理学报, 2025, 45(3): 850-857.

Chen Chizhou, Guo Hongxin. Volume Growth for Gradient Steady Solitons of the Extended Ricci Flow[J]. Acta mathematica scientia,Series A, 2025, 45(3): 850-857.

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