标题： 子静态流形的比较几何和加权等周不等式 显示英文标题

标题： Comparison geometry for substatic manifolds and a weighted Isoperimetric Inequality

摘要： 具有最小边界的次静态黎曼流形在广义相对论中作为满足零能量条件的静态时空的空间切片自然出现。 此外，它们是对非负里奇曲率的广泛推广。 在本文中，我们将证明此类中的各种几何结果，最终得出一个精确的加权等周不等式，该不等式量化了边界的面积最小性质。 其表述和证明将建立在部分源于与$\mathrm{CD}(0, 1)$度量新发现的共形联系的比较理论之上。 显示英文摘要

摘要： Substatic Riemannian manifolds with minimal boundary arise naturally in General Relativity as spatial slices of static spacetimes satisfying the Null Energy Condition. Moreover, they constitute a vast generalization of nonnegative Ricci curvature. In this paper we will prove various geometric results in this class, culminating in a sharp, weighted Isoperimetric inequality that quantifies the area minimizing property of the boundary. Its formulation and proof will build on a comparison theory partially stemming from a newly discovered conformal connection with $\mathrm{CD}(0, 1)$ metrics.