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On the average number of normals through points of a convex body
In 1944, Santal\'o asked about the average number of normals through a point
of a given convex body. Since then, numerous results appeared in the literature
about this problem. The aim of this paper is to give a concise summary of these
results, with some new, recent developments. We point out connections of this
problem to static equilibria of rigid bodies as well as to geometric partial
differential equations of surface evolution.Comment: 15 page