Ice flow models typically assume that ice is incompressible, a reasonable assumption because density changes are indeed small and have correspondingly effect on the overall mass balance of glaciers sheets. Given immense volume sheets, however, even relatively may influence global mean sea level to degree severely impacts humanity (Hauer others, 2020). Here, we quantify role gravitational compre...

For manifolds with a distinguished asymptotically flat end, we prove density theorem which produces harmonic asymptotics on the while allowing for points of incompleteness (or negative scalar curvature) away from this end. We use to improve “quantitative” version positive mass (in dimensions $$3\le n\le 7$$ ), obtained by last two named authors S.-T. Yau (J Diff Geom, 2021 (To appear)), where s...