We prove a Lipschitz approximation with superlinear error terms for integral currents $\omega$-minimizing the area functional, where $\omega$ is a modulus of continuity. We also present an almost monotonicity result for the density of these general almost area minimzing currents.
On the regularity of area minimizing currents at boundaries with arbitrary multiplicity
A monotonicity result under symmetry and Morse index constraints in the plane
A monotonicity result for the first Steklov-Dirichlet Laplacian eigenvalue
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