论文标题
强大的Brunn---inkowski不平等及其与CD条件的等效性
The strong Brunn--Minkowski inequality and its equivalence with the CD condition
论文作者
论文摘要
在本质上非分支度量测量空间的设置中，我们证明了曲率维度条件CD（K，N）之间的等效性，从Lott-sturm-villani的意义上，以及新引入的概念，我们称之为强大的Brunn-Minkowski不合适的SBM（K，k，n）。这种条件是广义的Brunn-Minkowski不平等BM（K，N）的加强，已知可以在CD（K，N）空间中保存。我们的结果是在CD（K，N）条件和BM（K，N）的有效性之间提供完全等价的第一步，我们最近在加权的Riemannian歧管框架中证明了这一点。
In the setting of essentially non-branching metric measure spaces, we prove the equivalence between the curvature dimension condition CD(K,N), in the sense of Lott--Sturm--Villani, and a newly introduced notion that we call strong Brunn--Minkowski inequality SBM(K,N). This condition is a reinforcement of the generalized Brunn--Minkowski inequality BM(K,N), which is known to hold in CD(K,N) spaces. Our result is a first step towards providing a full equivalence between the CD(K,N) condition and the validity of BM(K,N), which we have recently proved in the framework of weighted Riemannian manifolds.
