非常严格$CD(K,N)$ -空间的等价定义
Equivalent definitions of very strict $CD(K,N)$ -spaces
摘要：
我们证明了非常严格的$CD(K,N)$ -条件定义的等价性，一方面，（仅）使用熵泛函，另一方面，全位移凸类$\mathcal{DC}_N$。特别是，我们表明，假设凸性不等式的临界指数意味着它的所有更大的指数。我们还建立了最优输运映射的存在性非常严格的$CD(K,N)$ -空间有限的$N$。
英文摘要：
We show the equivalence of the definitions of very strict $CD(K,N)$ -condition defined, on one hand, using (only) the entropy functionals, and on the other, the full displacement convexity class $\mathcal{DC}_N$. In particular, we show that assuming the convexity inequalities for the critical exponent implies it for all the greater exponents. We also establish the existence of optimal transport maps in very strict $CD(K,N)$ -spaces with finite $N$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
