Envelopes created by pseudo-circle families in the Minkowski plane

TL;DR

This paper investigates the properties and problems related to envelopes formed by pseudo-circle families in the Minkowski plane, highlighting differences from Euclidean cases and providing comprehensive solutions.

Contribution

It offers the first complete analysis of envelope existence, representation, enumeration, and definitional relationships for pseudo-circles in Minkowski geometry.

Findings

Solved all four basic envelope problems in Minkowski plane

Identified key differences from Euclidean envelope properties

Established foundational results for pseudo-circle families

Abstract

In this paper, we address the topic of envelopes created by pseudo-circle families in the Minkowski plane, which exhibit some different properties when compared with the Euclidean case. We provide solutions to all four basic problems associated with these envelopes, namely the existence problem, representation problem, problem on the number of envelopes, and problem on the relationships of definitions.