The number of catenoids connecting two coaxial circles in Lorentz-Minkowski space

TL;DR

This paper investigates the number of catenoids connecting two coaxial circles in Lorentz-Minkowski space, considering different circle types and the causal character of the catenoids, providing a comprehensive classification.

Contribution

It offers a detailed classification of catenoids connecting coaxial circles in Lorentz-Minkowski space based on circle types and causal characters, extending classical minimal surface results.

Findings

Number of catenoids depends on circle types and causal character.

Classification includes spacelike and timelike catenoids.

Results generalize known Euclidean catenoid configurations.

Abstract

In 3-dimensional Lorentz-Minkowski space we determine the number of catenoids connecting two coaxial circles in parallel planes. This study is separated according to the types of circles and the causal character (spacelike and timelike) of the catenoid.