A new proof of the description of the convex hull of space curves with totally positive torsion

J. A. Jiménez Madrid, Paata Ivanisvili, Jaume de Dios Pont

Publication date: 30 January 2022

Abstract: We give new proofs of the description convex hulls of space curves

g a m m a : [a, b] m a p s t o m a t h b b R^{d}

having totally positive torsion. These are curves such that all the leading principal minors of

d i m e s d

matrix

(g a m m a^{'}, g a m m a^{″}, l d o t s, g a m m a^{(d)})

are positive. In particular, we recover parametric representation of the boundary of the convex hull, different formulas for its surface area and the volume of the convex hull, and the solution to a general moment problem corresponding to

g a m m a

.

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Inequalities and extremum problems involving convexity in convex geometry (52A40) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

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