Asymptotic Behavior of a Surface Implicitly Defined
Elena Campo Montalvo, Marián Fernández de Sevilla, Sonia Pérez-Dı́az · Mathematics · 2022
In this paper, we introduce the notion of infinity branches and approaching surfaces. We obtain an algorithm that compares the behavior at the infinity of two given algebraic surfaces that are defined by an irreducible polynomial. Furthermore, we show that if two surfaces have the same asymptotic behavior, the Hausdorff distance between them is finite. All these concepts are new and represent a great advance for the study of surfaces and their applications.