The metric entropy duality conjecture asserts universal comparison of translative covering numbers of origin-symmetric convex bodies
and their polar bodies. One full formulation asks for
constants 
such that, in every finite dimension,
Here 
are origin-symmetric convex bodies, 
are their polar
bodies, and the covering centers are unrestricted.
See also
Convex Body,
Cotype-Cotype Problem,
Polar Body,
Translative
Covering Number
Explore with Wolfram|Alpha
References
Artstein, S.; Milman, V.; and Szarek, S. J. "Duality
of Metric Entropy." Ann. Math. 159, 1313-1328, 2004. https://doi.org/10.4007/annals.2004.159.1313.
Cite this as:
Weisstein, Eric W. "Metric Entropy Duality
Conjecture." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/MetricEntropyDualityConjecture.html
Subject classifications
