Non-decreasable extremal Beltrami differentials of non-landslide type

TL;DR

This paper explores the deformation of extremal Beltrami differentials to produce non-unique, non-landslide, and non-decreasable examples, advancing understanding of their structure and properties.

Contribution

It introduces a method to deform uniquely-extremal Beltrami differentials into non-unique, non-landslide, and non-decreasable types, expanding the class of known extremal differentials.

Findings

Constructed non-unique extremal Beltrami differentials that are non-landslide and non-decreasable.

Demonstrated deformation techniques for extremal Beltrami differentials.

Expanded the understanding of the structure of extremal Beltrami differentials.

Abstract

In this paper, we deform a uniquely-extremal Beltrami differential into different non-decreasable Beltrami differentials, and then construct non-unique extremal Beltrami differentials such that they are both non-landslide and non-decreasable.