TY - JOUR
T1 - Powers and logarithms of convex bodies
AU - Milman, Vitali
AU - Rotem, Liran
N1 - Publisher Copyright:
© 2017 Académie des sciences
PY - 2017/9
Y1 - 2017/9
N2 - 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.
AB - 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.
UR - https://www.scopus.com/pages/publications/85029877168
U2 - 10.1016/j.crma.2017.09.002
DO - 10.1016/j.crma.2017.09.002
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AN - SCOPUS:85029877168
SN - 1631-073X
VL - 355
SP - 981
EP - 986
JO - Comptes Rendus Mathematique
JF - Comptes Rendus Mathematique
IS - 9
ER -