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We prove the multiplicity one theorem for min-max free boundary minimalhypersurfaces in compact manifolds with boundary of dimension between 3 and 7for generic metrics. To approach this, we develop existence and regularitytheory for free boundary hypersurface with prescribed mean curvature, whichincludes the regularity theory for minimizers, compactness theory, and ageneric min-max theory with Morse index bounds. As applications, we constructnew free boundary minimal hypersurfaces in the unit balls in Euclidean spacesand self-shrinkers of the mean curvature flows with arbitrarily large entropy.

Multiplicity one for min-max theory in compact manifolds with boundary and its applications