Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 31, No. 1, pp. 81-96 (2015)

A short review on the theory of generalized conics

Ábris Nagy

Hungarian Academy of Sciences and University of Debrecen

Abstract: Generalized conics are the level sets of functions measuring the average distance from a given set of points. This involves an extension of the concept of conics to the case of infinitely many focuses. The measuring of the average distance is realized via integration. Generalized conics recently have many interesting applications from Finsler geometry to geometric tomography. The aim of this survey paper is to collect the most important results concerning generalized conics.

Keywords: Generalized conic, Minkowski functional, geometric tomography.

Classification (MSC2000): 53-02; 53A04, 53A05

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