Entropy of convex hulls and Kuelbs-Li inequalities

Kley, Oliver GND

The leitmotif of this work can be described in quite a simple manner: Given three distinct points in the plane, one needs at most three disks of arbitrary radius to cover them. Those three points may be regarded to constitute the vertices of a triangle. Obviously, many more than three disks are necessary to cover the whole figure, and their number increases as their radii decrease. The triangle is the convex hull of its vertices. In this sense the question can be generalized: How many balls of certain radius are needed to cover the convex hull of a set of points in some linear normed space provided information about how many balls are needed to cover the original set?


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