AI 中文总结
研究四维时空零锥类空截面在保面积变化下的稳定性，通过引入相关概念，在主导能量条件下得出稳定截面霍金能量有非负下界等结论，还证明标准闵可夫斯基光锥唯一稳定截面是圆球。
AI 中文摘要
在本注记中，我们研究了零锥类空截面在保面积变化下的一种稳定性概念，该概念由克伦克和作者在先前工作中引入。这里，我们考虑四维时空中具有球形截面的零锥，并表明在主导能量条件成立的情况下，稳定截面的霍金能量有非负下界。与佩纽埃拉·迪亚兹最近的工作类似，我们表明在一个额外假设下，当且仅当稳定截面等距嵌入闵可夫斯基光锥时，霍金能量为零。作为主要结果，我们表明标准闵可夫斯基光锥的唯一稳定截面是圆球。
英文摘要
In this note we investigate a notion of stability for spacelike cross sections of a null cone under area preserving variations that has been introduced in previous work by Kröncke and the author. Here, we consider null cones with spherical cross sections in a $4$-dimensional spacetime and show that the Hawking energy of a stable cross section admits a non-negative lower bound provided the dominant energy condition holds. Similar to a recent work by Peñuela Diaz, we show that under an additional assumption the Hakwing energy is zero if and only if the stable cross section embeds isometrically into the Minkowski lightcone. As a main result, we show that the only stable cross sections of the standard Minkowski lightcone are round spheres.
