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arXiv · 2006.09472

Continuous quantitative Helly-type results

Tomás Fernandez Vidal·Daniel Galicer·Mariano Merzbacher
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Abstract

Brazitikos' results on quantititative Helly-type theorems (for the volume and for the diameter) rely on the work of Srivastava on sparsification of John's decompositions. We change this technique by a stronger recent result due to Friedland and Youssef. This, together with an appropriate selection in the accuracy of the approximation, allow us to obtain Helly-type versions which are sensitive to the number of convex sets involved.

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Tomás Fernandez Vidal, Daniel Galicer, Mariano Merzbacher. 2020-06-16. Continuous quantitative Helly-type results. https://arxiv.org/abs/2006.09472

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