标题： 好的测地线满足时空中曲率-维度条件 显示英文标题

标题： Good geodesics satisfying the timelike curvature-dimension condition

摘要： 设$(M,\mathsf{d},\mathfrak{m},\ll,\leq,\tau)$是一个因果闭合的，$\mathscr{K}$-整体双曲的，正则度量洛伦兹几何空间，并且满足 Cavalletti 和 Mondino 所定义的弱时序曲率维度条件$\smash{\mathrm{wTCD}_p^e(K,N)}$。我们证明了在$M$上概率测度的测地线的存在性，这些测地线满足定义$\smash{\mathrm{wTCD}_p^e(K,N)}$的熵半凸性不等式，并且相对于$\mathfrak{m}$的密度在时间上额外具有均匀的$L^\infty$性质。这成立而不需任何非分支假设。我们也讨论了在时序测度收缩性质下的类似结果。 显示英文摘要

摘要： Let $(M,\mathsf{d},\mathfrak{m},\ll,\leq,\tau)$ be a causally closed, $\mathscr{K}$-globally hyperbolic, regular measured Lorentzian geodesic space satisfying the weak timelike curvature-dimension condition $\smash{\mathrm{wTCD}_p^e(K,N)}$ in the sense of Cavalletti and Mondino. We prove the existence of geodesics of probability measures on $M$ which satisfy the entropic semiconvexity inequality defining $\smash{\mathrm{wTCD}_p^e(K,N)}$ and whose densities with respect to $\mathfrak{m}$ are additionally uniformly $L^\infty$ in time. This holds apart from any nonbranching assumption. We also discuss similar results under the timelike measure-contraction property.