Werner Georg Nowak - Estimating the critical determinants of a class of three-dimensional star bodies

cm:9470 - Communications in Mathematics, January 11, 2018, Volume 25 (2017), Issue 2 - https://doi.org/10.1515/cm-2017-0012
Estimating the critical determinants of a class of three-dimensional star bodies

Authors: Werner Georg Nowak

    In the problem of (simultaneous) Diophantine approximation in ℝ3 (in the spirit of Hurwitz’s theorem), lower bounds for the critical determinant of the special three-dimensional body K2 : (y2 + z2)(x2 + y2 + z2) ≤ 1 play an important role; see [1], [6]. This article deals with estimates from below for the critical determinant ∆ (Kc) of more general star bodies Kc : (y2 + z2)c/2(x2 + y2 + z2) ≤ 1 ; where c is any positive constant. These are obtained by inscribing into Kc either a double cone, or an ellipsoid, or a double paraboloid, depending on the size of c.


    Volume: Volume 25 (2017), Issue 2
    Published on: January 11, 2018
    Imported on: May 11, 2022
    Keywords: General Mathematics,[MATH]Mathematics [math]

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