## Regularity of weakly stable codimension 1 CMC varifolds

Neshan Wickramasekera

University of Cambridge; Member, School of Mathematics

January 15, 2019

The lecture will discuss recent joint work with C. Bellettini and O. Chodosh. The work taken together establishes sharp regularity conclusions, compactness and curvature estimates for any family of codimension 1 integral $n$-varifolds satisfying: (i) locally uniform mass and $L^{p}$ mean curvature bounds for some $p > n;$ (ii) two structural conditions and (iii) two variational hypotheses on the orientable regular parts, namely, stationarity and (weak) stability with respect to the area functional for volume preserving deformations (supported on the regular parts).