Elaborating on the similarity between the entropy power inequality and the Brunn-Minkowski inequality, Costa and Cover conjectured the 1n-concavity of the outer parallel volume of measurable sets as an analogue of the concavity of entropy power. We investigate this conjecture and study its relationship with geometric inequalities.
Bibliographical noteFunding Information:
The authors were supported in part by the Agence Nationale de la Recherche , project GeMeCoD ( ANR 2011 BS01 007 01 ).
- Entropy power
- Isoperimetric inequality
- Parallel set
- Parallel volume