Geodesic
Brunn--Minkowski type inequalities for conformal and Euclidean moments of domains
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2014), pp. 64-67.

Voir la notice de l'article provenant de la source Math-Net.Ru

We prove Brunn–Minkowski type inequalities for three new functionals which are power moments for conformal and Euclidean characteristics of domains.
Keywords: Brunn–Minkowski inequalities, hyperbolic metric coefficient, distance function. 
@article{IVM_2014_5_a6,
     author = {F. G. Avkhadiev and B. S. Timergaliev},
     title = {Brunn--Minkowski type inequalities for conformal and {Euclidean} moments of domains},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {64--67},
     publisher = {mathdoc},
     number = {5},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2014_5_a6/}
}
TY  - JOUR
AU  - F. G. Avkhadiev
AU  - B. S. Timergaliev
TI  - Brunn--Minkowski type inequalities for conformal and Euclidean moments of domains
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2014
SP  - 64
EP  - 67
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2014_5_a6/
LA  - ru
ID  - IVM_2014_5_a6
ER  - 
%0 Journal Article
%A F. G. Avkhadiev
%A B. S. Timergaliev
%T Brunn--Minkowski type inequalities for conformal and Euclidean moments of domains
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2014
%P 64-67
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2014_5_a6/
%G ru
%F IVM_2014_5_a6
F. G. Avkhadiev; B. S. Timergaliev. Brunn--Minkowski type inequalities for conformal and Euclidean moments of domains. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2014), pp. 64-67. http://geodesic.mathdoc.fr/item/IVM_2014_5_a6/

[1] Hadwiger H., “Konkave eikörperfunktionale und höhere trägheitsmomente”, Comment Math. Helv., 30 (1956), 285–296 | DOI | MR | Zbl

[2] Prékopa A., “Logarithmic concave measures with application to stochastic programming”, Acta Sci. Math. (Szeged), 32:3–4 (1971), 301–316 | MR | Zbl

[3] Leindler L., “On a certain converse of Hölder's inequality. II”, Acta Sci. Math. (Szeged), 33:3–4 (1972), 217–223 | MR | Zbl

[4] Brascamp H. J., Lieb E. H., “On extensions of the Brunn–Minkowski and Prékopa–Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation”, J. Func. Analysis, 22:4 (1976), 366–389 | DOI | MR | Zbl

[5] Borell C., “Diffusion equations and geometric inequalities”, Potential Anal., 12:1 (2000), 49–71 | DOI | MR | Zbl

[6] Gardner R. J., “The Brunn–Minkowski inequality”, Bull. Amer. Math. Soc., 39:3 (2002), 355–405 | DOI | MR | Zbl

[7] Barthe F., “The Brunn–Minkowski theorem and related geometric and functional inequalities”, Proc. Internat. Congress Math., v. II, Eur. Math. Soc., Zürich, 2006 | MR | Zbl

[8] Figalli A., Maggi F., Pratelli A., “A refined Brunn–Minkowski inequality for convex sets”, Ann. Inst. H. Poincaré Anal. Non Linéaire, 26:6 (2009), 2511–2519 | DOI | MR | Zbl

[9] Gardner R. J., Zvavitch A., “Gaussian Brunn–Minkowski inequalities”, Trans. Amer. Math. Soc., 362:10 (2010), 5333–5353 | DOI | MR | Zbl

[10] Lv S., “Dual Brunn–Minkowski inequality for volume differences”, Geom. Dedicata, 145 (2010), 169–180 | DOI | MR | Zbl

[11] Keady G., “On a Brunn–Minkowski theorem for a geometric domain functional considered by Avhadiev”, J. Inequal. Pure Appl. Math., 8:2, Article 33, 4 pp., (electronic) | MR

[12] Avkhadiev F. G., “Reshenie obobschennoi zadachi Sen-Venana”, Matem. sb., 189:12 (1998), 3–12 | DOI | MR | Zbl

[13] Goluzin G. M., Geometricheskaya teoriya funktsii kompleksnogo peremennogo, Nauka, M., 1966 | MR | Zbl

[14] Avkhadiev F. G., Wirths K.-J., Schwarz–Pick type inequalities, Birkhäuser Verlag, Basel–Boston–Berlin, 2009 | MR | Zbl

[15] Knothe H., “Contributions to the theory of convex bodies”, Michigan Math. J., 4 (1957), 39–52 | DOI | MR | Zbl

[16] Timergaliev B. S., “Neravenstvo Brunna–Minkovskogo dlya funktsionalov, svyazannykh s granichnymi momentami oblasti”, Itogovaya nauchno-obrazovatelnaya konferentsiya studentov KFU 2012 goda, Cb. statei, v. 5, 2012, 27–29