Lipschitz approximation for general almost area minimizing currents

TL;DR

This paper introduces a Lipschitz approximation method with superlinear error terms for area-minimizing currents under a Dini-continuous modulus, along with an almost monotonicity result for their density.

Contribution

It provides a novel Lipschitz approximation technique with superlinear error bounds and establishes an almost monotonicity property for general almost area-minimizing currents.

Findings

Lipschitz approximation with superlinear error terms for area-minimizing currents.

Almost monotonicity of the density of these currents.

Applicability under Dini continuity conditions.

Abstract

We prove a Lipschitz approximation with superlinear error terms for integral currents $\omega$-minimizing the area functional, where $\omega$ is a modulus of continuity satisfying a Dini condition. We also present an almost monotonicity result for the density of these general almost area minimzing currents.