Infinitesimally extremal Beltrami differentials of non-landslide type

TL;DR

This paper demonstrates the existence of infinitely many extremal Beltrami differentials of non-landslide type with non-constant modulus within certain infinitesimal classes, unless a unique extremal exists.

Contribution

It establishes the conditions under which infinitely many extremal Beltrami differentials exist in an infinitesimal class, expanding understanding of their structure.

Findings

Existence of infinitely many extremal Beltrami differentials of non-landslide type.

Non-constant modulus differentials can be infinitely many in a class.

Uniqueness of extremal differentials implies the absence of such infinity.

Abstract

In this paper, it is shown that there are infinitely many extremal Beltrami differentials of non-landside type and non-constant modulus in an infinitesimal equivalence class unless the class contains a unique extremal.