Regularity of Dirichlet nearly minimizing multiple-valued functions

TL;DR

This paper extends the concepts of Dirichlet quasiminimizers and related notions to multiple-valued functions, establishing Holder regularity and providing examples with various branch sets.

Contribution

It introduces new regularity results for Dirichlet nearly minimizing multiple-valued functions and expands the framework to include examples with complex branch sets.

Findings

Holder regularity of Dirichlet nearly minimizing multiple-valued functions

Examples of minimizers with various branch sets

Extension of quasiminimizer notions to multiple-valued functions

Abstract

In this paper, we extend the related notions of Dirichlet quasiminimizer, $\omega-$minimizer and almost minimizer to the framework of multiple-valued functions in the sense of Almgren and prove Holder regularity results. We also give examples of those minimizers with various branch sets.