A weak energy identity and the length of necks for a Sacks-Uhlenbeck $\alpha$-harmonic map sequence

TL;DR

This paper establishes a weak energy identity for Sacks-Uhlenbeck approximations of harmonic maps and computes the length of neck regions, advancing understanding of the energy concentration phenomena in geometric analysis.

Contribution

It introduces a weak energy identity for the Sacks-Uhlenbeck approximation and provides a method to calculate neck lengths, which are new insights in the study of harmonic map sequences.

Findings

Proves a weak energy identity for Sacks-Uhlenbeck approximations.

Calculates the length of neck regions in harmonic map sequences.

Enhances understanding of energy concentration and neck formation.

Abstract

We will give a weak energy identity for Sacks-Uhlenbeck approximation of harmonic maps and calculate the length of the necks.