A spectral study of the Minkowski Curve

TL;DR

This paper constructs an explicit Laplacian on the Minkowski curve, analyzing its spectrum through spectral decimation, and highlights the geometric features influencing the energy forms.

Contribution

It provides a novel explicit construction of a Laplacian on the Minkowski curve and analyzes its spectrum using spectral decimation.

Findings

Explicit Laplacian construction on Minkowski curve

Spectrum obtained via spectral decimation

Energy forms reflect geometric structure

Abstract

In the following, we give an explicit construction of a Laplacian on the Minkowski curve, with energy forms that bear the geometric characteristic of the structure. The spectrum of the Laplacian is obtained by means of spectral decimation.