# Higher order neck analysis of harmonic maps and its applications

## TL;DR

This paper refines estimates in the neck regions of harmonic maps during blow-up sequences, revealing the shape of the neck center and deriving related inequalities about nullity and index.

## Contribution

It introduces new refined estimates in the neck region of harmonic maps, enabling detailed analysis of blow-up behavior and related spectral inequalities.

## Key findings

- Refined estimates in the neck region during harmonic map blow-up
- Identification of the shape of the neck center
- Inequality relating nullity and index during blow-up

## Abstract

In this paper, we prove some refined estimate in the neck region when a sequence of harmonic maps from surfaces blow up. The new estimate allows us to see the shape of the center of the neck region. As an application, we prove an inequality about the nullity and index when blow-up occurs.