黎曼叶理的横向ft -熵

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications Pub Date : 2025-09-15 DOI:10.1016/j.jmaa.2025.130070

Dexie Lin

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引用次数: 0

摘要

本文从佩雷尔曼的工作中得到启发，引入黎曼叶上的熵泛函。我们将其梯度流与横里奇流通过保持叶理的微分同态联系起来。我们证明了它沿横向里奇流是单调的。此外，受方福全和张玉光工作的启发，我们给出了任何余维-4黎曼叶化存在横向爱因斯坦度规的充分条件。

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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Transverse FT-entropy for Riemannian foliations

In this paper, we introduce an entropy functional on Riemannian foliations, inspired by the work of Perelman. We relate its gradient flow to the transverse Ricci flow via the foliation preserving diffeomorphisms. We show that it is monotonic along the transverse Ricci flow. Moreover, inspired by the work of Fuquan Fang and Yuguang Zhang, we give a sufficient condition for any codimension-4 Riemannian foliation to admit the transverse Einstein metric.

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来源期刊

Journal of Mathematical Analysis and Applications 数学-数学

CiteScore

2.50

自引率

7.70%

发文量

790

审稿时长

6 months

期刊介绍： The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Papers are sought which employ one or more of the following areas of classical analysis: • Analytic number theory • Functional analysis and operator theory • Real and harmonic analysis • Complex analysis • Numerical analysis • Applied mathematics • Partial differential equations • Dynamical systems • Control and Optimization • Probability • Mathematical biology • Combinatorics • Mathematical physics.