Deformations of harmonic function germs

TL;DR

This paper investigates the classification of singularities in harmonic function germs with two variables, focusing on how Laplacian actions influence their right-equivalence classifications.

Contribution

It introduces a new approach to classify harmonic function germs by analyzing the multiple actions of the Laplacian operator.

Findings

Laplacian actions are crucial for classifying harmonic function germs.

A framework for understanding singularities with harmonic leading terms is developed.

The classification scheme enhances understanding of harmonic singularities.

Abstract

We study the classification problem of singularities of function-germs with harmonic leading terms of two variables under the right-equivalence. We observe that the multiple actions of Laplacian appear for the classifications of such class of function-germs.