In this web content, Dong and Song have proved a conjecture formulated by Huisken and Ilmanen in 2001. The conjecture states that as the mass of a space approaches zero, its curvature must also approach zero. However, this scenario is complicated by the presence of bubbles and spikes. Dong and Song have shown that these troublesome appendages can be removed in such a way that the remaining space is close to flat. They use a concept called scalar curvature to summarize the full curvature in all directions. This work provides strong evidence of how scalar curvature controls the geometry of space.
https://www.quantamagazine.org/a-century-later-new-math-smooths-out-general-relativity-20231130/