Noncollapsing via constant mean curvature or isoperimetric structures

Investigate noncollapsing conditions formulated using constant mean curvature surfaces or isoperimetric regions that, together with nonnegative scalar curvature, ensure favorable compactness and volume behavior under Sormani–Wenger intrinsic flat convergence.

Background

The authors point to results of Portegies, Jauregui–Lee, and Jauregui–Lee–Perales on SWIF-converging sequences with volume convergence, suggesting these may be leveraged with CMC or isoperimetric-based noncollapsing hypotheses.

Such geometric conditions could provide alternative mechanisms to preclude collapsing and disappearing regions in the limit.