Asymptotic Behavior of a Surface Implicitly Defined

Elena Campo-Montalvo, Marián Fernández de Sevilla and Sonia Pérez-Díaz
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Elena Campo-Montalvo: Departamento de Automática, Universidad de Alcalá, E-28871 Madrid, Spain
Marián Fernández de Sevilla: Departamento de Automática, Universidad de Alcalá, E-28871 Madrid, Spain
Sonia Pérez-Díaz: Departamento de Automática, Universidad de Alcalá, E-28871 Madrid, Spain

Mathematics, 2022, vol. 10, issue 9, 1-19

Abstract: 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.

Keywords: algebraic surfaces implicitly defined; infinity branch; convergent branch; asymptotic behavior; approaching surfaces (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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