2020/06/16 by T. Vidal, Vidal, Tomás Fernandez, Daniel Galicer +3
Computer Science · Mathematics · #52A23 #52A35 #52A38 #52A40 #FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG) #Numerical methods in inverse problems #Optimization and Variational Analysis #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.2006.09472
openalex publication_date 2020/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.