Do we have enough examples of convex bodies that we truly understand? Is out standard set of examples diverse enough to understand convexity? In this note, we will dramatically increase our set of examples. More specifically, we will present several new constructions of convex bodies: the geometric mean of two convex bodies, the power function Kα (which in general exists only for |α|≤1), and even the logarithm logK.
|Translated title of the contribution||Powers and logarithms of convex bodies|
|Number of pages||6|
|Journal||Comptes Rendus Mathematique|
|State||Published - Sep 2017|
Bibliographical noteFunding Information:
The first named author is supported by ISF grant number 519/17 , and the second named author is supported by an AMS–Simons Travel Grant. Both authors are also supported by BSF grant number 2016050 . Part of the research was conducted while the authors were in residence at the Mathematical Sciences Research Institute in Berkeley, California, supported by NSF grant DMS-1440140 .
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