Higher derivatives of length functions along earthquake deformations

TL;DR

This paper computes higher derivatives of length functions on Teichmuller space during earthquake deformations, extending known formulas for first and second derivatives to higher orders.

Contribution

It generalizes the existing cosine and sine formulas for first and second derivatives to higher derivatives in earthquake deformations.

Findings

Derived explicit formulas for higher derivatives of length functions.

Extended classical derivative formulas to higher orders.

Provides tools for analyzing Teichmuller space dynamics.

Abstract

We calculate the higher derivatives of length functions on Teichmuller space along earthquake deformations. This generalizes the cosine formula for the first derivative by Kerckhoff and Wolpert and the sine formula for second derivative by Wolpert.