On the analogue of the concavity of entropy power in the Brunn–Minkowski theory
Tài liệu tham khảo
Ané, 2000, Sur les inégalités de Sobolev logarithmiques, vol. 10
Ambrosio, 2008, Outer Minkowski content for some classes of closed set, Math. Ann., 342, 727, 10.1007/s00208-008-0254-z
Blachman, 1965, The convolution inequality for entropy powers, IEEE Trans. Inform. Theory, IT-11, 267, 10.1109/TIT.1965.1053768
Bobkov, 2012, Reverse Brunn–Minkowski and reverse entropy power inequalities for convex measures, J. Funct. Anal., 262, 3309, 10.1016/j.jfa.2012.01.011
Costa, 1985, A new entropy power inequality, IEEE Trans. Inform. Theory, 31, 751, 10.1109/TIT.1985.1057105
Costa, 1984, On the similarity of the entropy power inequality and the Brunn–Minkowski inequality, IEEE Trans. Inform. Theory, 30, 837, 10.1109/TIT.1984.1056983
Cover, 1991, Information theoretic inequalities, IEEE Trans. Inform. Theory, 37, 1501, 10.1109/18.104312
Dembo, 1990
Federer, 1969
Fiala, 1941, Le problème des isopérimètres sur les surfaces ouvertes à courbure positive, Comment. Math. Helv., 13, 293, 10.1007/BF01378068
Fradelizi, 2003, Some inequalities about mixed volumes, Israel J. Math., 135, 157, 10.1007/BF02776055
Guleryuz, 2002, Information-theoretic inequalities for contoured probability distributions, IEEE Trans. Inform. Theory, 48, 2377, 10.1109/TIT.2002.800496
Gorbovickis, 2013, Strict Kneser–Poulsen conjecture for large radii, Geom. Dedicata, 162, 95, 10.1007/s10711-012-9718-0
Kampf, 2012, The parallel volume at large distances, Geom. Dedicata, 160, 47, 10.1007/s10711-011-9669-x
Kampf, 2011
Kampf, 2013, Large parallel volumes of finite and compact sets in d-dimensional Euclidean space, Doc. Math., 18, 275, 10.4171/dm/397
Marsiglietti
Rataj, 2009, On the expected surface area of the Wiener sausage, Math. Nachr., 282, 591, 10.1002/mana.200610757
Schneider, 1975, A measure of convexity for compact sets, Pacific J. Math., 58, 617, 10.2140/pjm.1975.58.617
Schneider, 1993, Convex Bodies: The Brunn–Minkowski Theory, vol. 44
Stam, 1959, Some inequalities satisfied by the quantities of information of Fisher and Shannon, Inf. Control, 2, 101, 10.1016/S0019-9958(59)90348-1
Stachó, 1976, On the volume function of parallel sets, Acta Sci. Math., 38, 365
Szarek, 2000, Shannon's entropy power inequality via restricted Minkowski sums, vol. 1745, 257
Villani, 2000, A short proof of the “concavity of entropy power”, IEEE Trans. Inform. Theory, 46, 1695, 10.1109/18.850718