论文标题
良好的测量学满足及时的曲率维度条件
Good geodesics satisfying the timelike curvature-dimension condition
论文作者
论文摘要
令$（m，\ mathsf {d}，\ mathfrak {m}，\ ll，\ leq，τ）$是因果封闭，$ \ mathscr {k} $ - 全球夸张，定期测量的lorentzian lorentzian geodesic space满足弱的时脉度曲率维度约束条件$ \ smash {\ mathrm {wtcd} _p^e（k，n）} $在Cavalletti和Mondino的意义上。我们证明了$ m $上的概率度量的存在，这些概率度量满足了定义$ \ smash {\ mathrm {wtcd} _p^e（k，n）} $的entopic semiconvexity不平等，并且其密度与$ \ nathfrak {m} $是附加的$ l^fiftty $ l^。除了任何非分支假设外，这都具有。我们还讨论了定时度量收缩属性下的类似结果。
Let $(M,\mathsf{d},\mathfrak{m},\ll,\leq,τ)$ 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.
