Generalized flatness constants, spanning lattice polytopes, and the Gromov width

In this paper we motivate some new directions of research regarding the lattice width of convex bodies. We show that convex bodies of sufficiently large width contain a unimodular copy of a standard simplex. Following an argument of Eisenbrand and Shmonin, we prove that every lattice polytope contai...

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Veröffentlicht in:	Manuscripta mathematica 2023-01, Vol.170 (1-2), p.147-165
Hauptverfasser:	Averkov, Gennadiy, Hofscheier, Johannes, Nill, Benjamin
Format:	Artikel
Sprache:	eng
Schlagworte:	Algebraic Geometry Calculus of Variations and Optimal Control Optimization Convexity Flatness Geometry Lie Groups Lower bounds Mathematics Mathematics and Statistics Number Theory Polytopes Topological Groups
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