A short proof for the interior H\"{o}lder continuity of two-dimensional stationary Q-valued maps

TL;DR

This paper provides a concise proof demonstrating the interior H"{o}lder continuity of two-dimensional stationary Q-valued maps, utilizing a blow-up argument, monotonicity formula, and oscillation estimates.

Contribution

It introduces a simplified proof for regularity of stationary Q-valued maps in two dimensions, combining existing techniques in a novel way.

Findings

Establishes interior H"{o}lder continuity for two-dimensional stationary Q-valued maps.

Uses a blow-up argument based on the frequency function's monotonicity.

Leverages conformality and oscillation estimates for the proof.

Abstract

The aim of this article is to present a concise proof for the interior H\"{o}lder continuity of two-dimensional stationary Q-valued maps. The proof employs a blow-up argument based on the monotonicity formula for the frequency function, along with the oscillation estimate from the author's previous article, which leverages the conformality of the modified maps.