CONTINUOUS QUANTITATIVE HELLY-TYPE RESULTS

Tomás Fernandez Vidal,Daniel Galicer,Mariano Merzbacher

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY（2022）

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摘要

Brazitikos' results on quantitative 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 tool by a stronger recent result due to Friedland and Youssef which, together with an appropriate selection in the accuracy of the approximation, allows us to obtain Helly-type versions which are sensitive to the number of convex sets involved.

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关键词

Helly-type results, convex bodies, approximate John's decomposition

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