Preservation of structures under aggregation functions is an active area research with applications in many fields. Among such structures, min-subgroups play important role, for instance, mathematical morphology, where they can be used to model translation invariance. Aggregation has only been studied binary functions. However, results concerning preservation the min-subgroup structure aggregat...

We study min–max theory for the area functional among hypersurfaces constrained in a smooth manifold with boundary. A Schoen–Simon-type regularity result is proved integral varifolds which satisfy variational inequality and restricts to stable minimal hypersurface interior. Based on this, we show that any admissible family of sweepouts $$\Pi $$ compact boundary, there always exists closed $$C^{...