标题： 几何常数在变耦合参数扩展 Ricci 流下的演化与单调性 显示英文标题

标题： Evolution and Monotonicity of Geometric Constants under Extended Ricci Flows with Variable Coupling Parameters

摘要： 本文探讨了在扩展里奇流框架内几何常数的演化和单调性，结合了可变耦合参数。 在哈密顿基础里奇流及List（2008）后续扩展的基础上，我们通过改变影响度量和标量场之间相互作用的参数，对扩展里奇流进行了修改。 具体而言，我们修改了控制几何常数演化方程的系数，从而在分析中引入了新的自由度。 主要贡献包括推导出在扩展和归一化扩展里奇流下修改后的几何常数lambda的演化公式，并证明了保持单调性的条件。 显示英文摘要

摘要： This paper explores the evolution and monotonicity of geometric constants within the framework of extended Ricci flows, incorporating variable coupling parameters. Building on Hamiltons foundational Ricci flow and subsequent extensions by List (2008), we introduce modifications to the extended Ricci flow by varying parameters that affect the interaction between the metric and scalar fields. Specifically, we modify the coefficients in the evolution equations governing geometric constants, thereby introducing new degrees of freedom in the analysis. The primary contributions include deriving evolution formulas for the modified geometric constant lambda under the extended and normalized extended Ricci flows, and proving conditions under which monotonicity is maintained.