Singularities of functions with harmonic leading terms of two variables

TL;DR

This paper classifies singularities of two-variable functions with harmonic leading terms up to order 7, revealing the role of Laplacian actions in their classification under right-equivalence.

Contribution

It provides a detailed classification of singularities with harmonic leading terms up to order 7, highlighting the influence of Laplacian actions.

Findings

Classification of singularities up to order 7

Identification of Laplacian actions in classification

Enhanced understanding of harmonic function-germs

Abstract

We study the classification problem of singularities of function-germs with harmonic leading terms of two variables under the right-equivalence. We study the classification in the cases that the order of function-germs is at most 7. Moreover, we observe that the multiple actions of Laplacian appear for the classifications of such class of function-germs.