Displaying similar documents to “On a conjecture by Auerbach”

Minimal pairs of bounded closed convex sets

J. Grzybowski, R. Urbański (1997)

Studia Mathematica

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The existence of a minimal element in every equivalence class of pairs of bounded closed convex sets in a reflexive locally convex topological vector space is proved. An example of a non-reflexive Banach space with an equivalence class containing no minimal element is presented.

Minimal pairs of compact convex sets

Diethard Pallaschke, Ryszard Urbański (2004)

Banach Center Publications

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Pairs of compact convex sets naturally arise in quasidifferential calculus as sub- and superdifferentials of a quasidifferentiable function (see Dem86). Since the sub- and superdifferentials are not uniquely determined, minimal representations are of special importance. In this paper we give a survey on some recent results on minimal pairs of closed bounded convex sets in a topological vector space (see PALURB). Particular attention is paid to the problem of characterizing minimal representatives...

Around Podewski's conjecture

Krzysztof Krupiński, Predrag Tanović, Frank O. Wagner (2013)

Fundamenta Mathematicae

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A long-standing conjecture of Podewski states that every minimal field is algebraically closed. Known in positive characteristic, it remains wide open in characteristic zero. We reduce Podewski's conjecture to the (partially) ordered case, and we conjecture that such fields do not exist. We prove the conjecture in case the incomparability relation is transitive (the almost linear case). We also study minimal groups with a (partial) order, and give a complete classification...

Minimal pairs of bounded closed convex sets as minimal representations of elements of the Minkowski-Rådström-Hörmander spaces

Jerzy Grzybowski, Diethard Pallaschke, Ryszard Urbański (2009)

Banach Center Publications

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The theory of minimal pairs of bounded closed convex sets was treated extensively in the book authored by D. Pallaschke and R. Urbański, Pairs of Compact Convex Sets, Fractional Arithmetic with Convex Sets. In the present paper we summarize the known results, generalize some of them and add new ones.

Minimal Niven numbers

H. Fredricksen, E. J. Ionascu, F. Luca, P. Stănică (2008)

Acta Arithmetica

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Minimality in asymmetry classes

Michał Wiernowolski (1997)

Studia Mathematica

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We examine minimality in asymmetry classes of convex compact sets with respect to inclusion. We prove that each class has a minimal element. Moreover, we show there is a connection between asymmetry classes and the Rådström-Hörmander lattice. This is used to present an alternative solution to the problem of minimality posed by G. Ewald and G. C. Shephard in [4].

A conjecture on minimal surfaces

Gianfranco Cimmino (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Simple computations support the conjecture that a small spherical surface with its center on a minimal surface cannot be divided by the minimal surface into two portions with different area.