A Refined Brunn-Minkowski Inequality for Convex Sets
Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 6, pp. 2511-2519. 
@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},
     pages = {2511--2519},
     publisher = {Elsevier},
     volume = {26},
     number = {6},
     year = {2009},
     doi = {10.1016/j.anihpc.2009.07.004},
     mrnumber = {2569906},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2009.07.004/}
}
TY  - JOUR
AU  - Figalli, A.
AU  - Maggi, F.
AU  - Pratelli, A.
TI  - A Refined Brunn-Minkowski Inequality for Convex Sets
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2009
SP  - 2511
EP  - 2519
VL  - 26
IS  - 6
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.anihpc.2009.07.004/
DO  - 10.1016/j.anihpc.2009.07.004
LA  - en
ID  - AIHPC_2009__26_6_2511_0
ER  - 
%0 Journal Article
%A Figalli, A.
%A Maggi, F.
%A Pratelli, A.
%T A Refined Brunn-Minkowski Inequality for Convex Sets
%J Annales de l'I.H.P. Analyse non linéaire
%D 2009
%P 2511-2519
%V 26
%N 6
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.anihpc.2009.07.004/
%R 10.1016/j.anihpc.2009.07.004
%G en
%F 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) no. 6, pp. 2511-2519. doi : 10.1016/j.anihpc.2009.07.004. http://www.numdam.org/articles/10.1016/j.anihpc.2009.07.004/

[1] Ambrosio L., Fusco N., Pallara D., Functions of Bounded Variation and Free Discontinuity Problems, Oxford Math. Monogr., The Clarendon Press, Oxford University Press, New York, 2000. | MR | Zbl

[2] Brenier Y., Décomposition Polaire Et Réarrangement Monotone Des Champs De Vecteurs, C. R. Acad. Sci. Paris Sér. I Math. 305 (19) (1987) 805-808. | MR | Zbl

[3] Brenier Y., Polar Factorization and Monotone Rearrangement of Vector-Valued Functions, Comm. Pure Appl. Math. 44 (4) (1991) 375-417. | MR | Zbl

[4] Burago Y. D., Zalgaller V. A., Geometric Inequalities, Springer, New York, 1988, Russian original: 1980. | MR | Zbl

[5] Caffarelli L. A., The Regularity of Mappings With a Convex Potential, J. Amer. Math. Soc. 5 (1) (1992) 99-104. | MR | Zbl

[6] Caffarelli L. A., Boundary Regularity of Maps With Convex Potentials. II, Ann. of Math. (2) 144 (3) (1996) 453-496. | MR | Zbl

[7] Diskant V. I., Stability of the Solution of a Minkowski Equation, Sibirsk. Mat. Zh. 14 (1973) 669-673, 696 (in Russian). | MR | Zbl

[8] Evans L. C., Gariepy R. F., Measure Theory and Fine Properties of Functions, Stud. Adv. Math., CRC Press, Boca Raton, FL, 1992, viii+268 pp. | MR | Zbl

[9] Federer H., Geometric Measure Theory, Grundlehren Math. Wiss., vol. 153, Springer-Verlag New York Inc., New York, 1969, xiv+676 pp. | MR | Zbl

[10] A. Figalli, F. Maggi, A. Pratelli, A mass transportation approach to quantitative isoperimetric inequalities, submitted for publication.

[11] Gardner R. J., The Brunn-Minkowski Inequality, Bull. Amer. Math. Soc. (N.S.) 39 (3) (2002) 355-405. | MR | Zbl

[12] Groemer H., On the Brunn-Minkowski Theorem, Geom. Dedicata 27 (3) (1988) 357-371. | MR | Zbl

[13] Hadwiger H., Ohmann D., Brunn-Minkowskischer Satz Und Isoperimetrie, Math. Z. 66 (1956) 1-8. | MR | Zbl

[14] Henstock R., Macbeath A. M., On the Measure of Sum Sets, I. the Theorems of Brunn, Minkowski and Lusternik, Proc. London Math. Soc. 3 (1953) 182-194. | MR | Zbl

[15] John F., An Inequality for Convex Bodies, Univ. Kentucky Res. Club Bull. 8 (1942) 8-11. | MR | Zbl

[16] Mccann R. J., A Convexity Principle for Interacting Gases, Adv. Math. 128 (1) (1997) 153-179. | MR | Zbl

[17] Ruzsa I. Z., The Brunn-Minkowski Inequality and Nonconvex Sets, Geom. Dedicata 67 (3) (1997) 337-348. | MR | Zbl

[18] Schneider R., On the General Brunn-Minkowski Theorem, Beitrage Algebra Geom. 34 (1) (1993) 1-8. | MR | Zbl

[19] Villani C., Topics in Optimal Transportation, Grad. Stud. Math., vol. 58, Amer. Math. Soc., Providence, RI, 2003, xvi+370 pp. | MR | Zbl

Cité par Sources :