Bubbling with L2-almost constant mean curvature and an Alexandrov-type theorem for crystals - Delgadino, MG; Maggi, F; Mihaila, C; Neumayer, R (Springer Nature, 2018)
A compactness theorem for volume-constrained almost-critical points of elliptic integrands is proven. The result is new even for the area functional, as almost-criticality is measured in an integral rather than in a uniform sense. Two main applications of the compactness theorem are discussed. First, we obtain a description of critical points/local minimizers of elliptic energies interacting with a confinement potential. Second, we prove an Alexandrov-type theorem for crystalline isoperimetric problems.