AI 中文总结
本研究引入加权中间里奇曲率，建立其下界的等价刻画，推广相关结果并对比不同学者的刻画，为几何分析领域提供了新的理论进展。
AI 中文摘要
我们引入了加权中间里奇曲率的版本，并建立了其下界的若干等价刻画。作为应用，我们通过推导内在维数演化变分不等式及对应的热流Wasserstein收缩估计，推广了Aishwarya–Rotem–Shenfeld [arXiv:2509.23399v1]的结果；还通过低维最优传输，将我们的刻画与Ketterer–Mondino [arXiv:1610.03339v3]的刻画进行了比较。
英文摘要
We introduce a weighted version of intermediate Ricci curvature and establish several equivalent characterizations of its lower bound. As an application, we generalize the results of Aishwarya--Rotem--Shenfeld [arXiv:2509.23399v1] by deriving intrinsic-dimensional evolution variational inequalities and the corresponding Wasserstein contraction estimates for the heat flow. We also compare our characterization with that of Ketterer--Mondino [arXiv:1610.03339v3] via lower-dimensional optimal transport.
Comments60 pages
