Classification of Complete Expanding Gradient Weighted Yamabe Solitons

IF 1.2 3区数学 Q3 MATHEMATICS, APPLIED

Mathematical Physics, Analysis and Geometry Pub Date : 2025-11-05 DOI:10.1007/s11040-025-09536-w

Rong Mi

引用次数: 0

Abstract

In this article, we study geometric and analytical features of complete expanding gradient weighted Yamabe solitons, which are self-similar solutions of the weighted Yamabe flow. We show that if the weighted scalar curvature is greater than the soliton constant by an arbitrarily small positive constant, then the soliton is trivial. In contrast, if the weighted scalar curvature is less than the soliton constant by an arbitrarily small positive constant, then the soliton is rotationally symmetric. In addition, we completely classify nontrivial complete expanding gradient weighted Yamabe soliton under some assumed conditions.

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完全展开梯度加权Yamabe孤子的分类

本文研究了完全扩展梯度加权Yamabe孤子的几何特征和解析特征，这些孤子是加权Yamabe流的自相似解。我们证明如果加权标量曲率比孤子常数大一个任意小的正常数，那么孤子是平凡的。相反，如果加权标量曲率比孤子常数小一个任意小的正常数，则孤子是旋转对称的。此外，在一些假设条件下，我们对非平凡完全展开梯度加权Yamabe孤子进行了完全分类。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Physics, Analysis and Geometry 数学-物理：数学物理

CiteScore

2.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： MPAG is a peer-reviewed journal organized in sections. Each section is editorially independent and provides a high forum for research articles in the respective areas. The entire editorial board commits itself to combine the requirements of an accurate and fast refereeing process. The section on Probability and Statistical Physics focuses on probabilistic models and spatial stochastic processes arising in statistical physics. Examples include: interacting particle systems, non-equilibrium statistical mechanics, integrable probability, random graphs and percolation, critical phenomena and conformal theories. Applications of probability theory and statistical physics to other areas of mathematics, such as analysis (stochastic pde''s), random geometry, combinatorial aspects are also addressed. The section on Quantum Theory publishes research papers on developments in geometry, probability and analysis that are relevant to quantum theory. Topics that are covered in this section include: classical and algebraic quantum field theories, deformation and geometric quantisation, index theory, Lie algebras and Hopf algebras, non-commutative geometry, spectral theory for quantum systems, disordered quantum systems (Anderson localization, quantum diffusion), many-body quantum physics with applications to condensed matter theory, partial differential equations emerging from quantum theory, quantum lattice systems, topological phases of matter, equilibrium and non-equilibrium quantum statistical mechanics, multiscale analysis, rigorous renormalisation group.