@article{AIHPC_2009__26_6_2511_0, author = {Figalli, A. and Maggi, F. and Pratelli, A.}, title = {A Refined Brunn-Minkowski Inequality for Convex Sets}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, volume = {26}, year = {2009}, pages = {2511-2519}, doi = {10.1016/j.anihpc.2009.07.004}, mrnumber = {2569906}, zbl = {pre05649884}, language = {en}, url = {http://dml.mathdoc.fr/item/AIHPC_2009__26_6_2511_0} }
Figalli, A.; Maggi, F.; Pratelli, A. A Refined Brunn-Minkowski Inequality for Convex Sets. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) pp. 2511-2519. doi : 10.1016/j.anihpc.2009.07.004. http://gdmltest.u-ga.fr/item/AIHPC_2009__26_6_2511_0/
[1] Functions of Bounded Variation and Free Discontinuity Problems, Oxford Math. Monogr., The Clarendon Press, Oxford University Press, New York, 2000. | MR 1857292 | Zbl 0957.49001
, , ,[2] Décomposition Polaire Et Réarrangement Monotone Des Champs De Vecteurs, C. R. Acad. Sci. Paris Sér. I Math. 305 (19) (1987) 805-808. | MR 923203 | Zbl 0652.26017
,[3] Polar Factorization and Monotone Rearrangement of Vector-Valued Functions, Comm. Pure Appl. Math. 44 (4) (1991) 375-417. | MR 1100809 | Zbl 0738.46011
,[4] Geometric Inequalities, Springer, New York, 1988, Russian original: 1980. | MR 936419 | Zbl 0633.53002
, ,[5] The Regularity of Mappings With a Convex Potential, J. Amer. Math. Soc. 5 (1) (1992) 99-104. | MR 1124980 | Zbl 0753.35031
,[6] Boundary Regularity of Maps With Convex Potentials. II, Ann. of Math. (2) 144 (3) (1996) 453-496. | MR 1426885 | Zbl 0916.35016
,[7] Stability of the Solution of a Minkowski Equation, Sibirsk. Mat. Zh. 14 (1973) 669-673, 696 (in Russian). | MR 333988 | Zbl 0264.52007
,[8] Measure Theory and Fine Properties of Functions, Stud. Adv. Math., CRC Press, Boca Raton, FL, 1992, viii+268 pp. | MR 1158660 | Zbl 0804.28001
, ,[9] Geometric Measure Theory, Grundlehren Math. Wiss., vol. 153, Springer-Verlag New York Inc., New York, 1969, xiv+676 pp. | MR 257325 | Zbl 0176.00801
,[10] A. Figalli, F. Maggi, A. Pratelli, A mass transportation approach to quantitative isoperimetric inequalities, submitted for publication.
[11] The Brunn-Minkowski Inequality, Bull. Amer. Math. Soc. (N.S.) 39 (3) (2002) 355-405. | MR 1898210 | Zbl 1019.26008
,[12] On the Brunn-Minkowski Theorem, Geom. Dedicata 27 (3) (1988) 357-371. | MR 960207 | Zbl 0652.52009
,[13] Brunn-Minkowskischer Satz Und Isoperimetrie, Math. Z. 66 (1956) 1-8. | MR 82697 | Zbl 0071.38001
, ,[14] On the Measure of Sum Sets, I. the Theorems of Brunn, Minkowski and Lusternik, Proc. London Math. Soc. 3 (1953) 182-194. | MR 56669 | Zbl 0052.18302
, ,[15] An Inequality for Convex Bodies, Univ. Kentucky Res. Club Bull. 8 (1942) 8-11. | MR 8157 | Zbl 0061.38301
,[16] A Convexity Principle for Interacting Gases, Adv. Math. 128 (1) (1997) 153-179. | MR 1451422 | Zbl 0901.49012
,[17] The Brunn-Minkowski Inequality and Nonconvex Sets, Geom. Dedicata 67 (3) (1997) 337-348. | MR 1475877 | Zbl 0888.52011
,[18] On the General Brunn-Minkowski Theorem, Beitrage Algebra Geom. 34 (1) (1993) 1-8. | MR 1239273 | Zbl 0788.52008
,[19] Topics in Optimal Transportation, Grad. Stud. Math., vol. 58, Amer. Math. Soc., Providence, RI, 2003, xvi+370 pp. | MR 1964483 | Zbl 1106.90001
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