publication . Preprint . 2010

Convex Bodies With Minimal Volume Product in R^2 --- A New Proof

Lin, Youjiang;
Open Access English
  • Published: 10 Mar 2010
Comment: 14pages, 4 figures, 14 conferences
free text keywords: Mathematics - Metric Geometry, 52A10, 52A40
Download from

[1] J. Bourgain, V. D. Milman, New volume ratio properties for convex symmetric bodies in Rn. Invent. Math. 88 (1987),319-340. MR0880954 (88f:52013)

[2] Y. Gordon, M. Meyer and S. Reisner, Zonoids with minimal volumeCproduct - a new proof. Proceedings of the American Math. Soc. 104 (1988), 273-276. MR0958082 (89i:52015)

[3] G. Kuperberg, From the Mahler Conjecture to Gauss Linking Integrals. Geometric And Functional Analysis, 18 (2008), 870-892. MR2438998 (2009i:52005)

[4] K. Mahler, Ein Ubertragungsprinzip fur konvexe Korper. Casopis Pyest. Mat. Fys. 68, (1939), 93-102. MR0001242 (1,202c)

[5] E. Lutwak, G. Zhang, Blaschke-Santalo´ inequalities. J. Differential Geom. 47 (1997), 1-16. 52A40 MR1601426 (2000c:52011)

[6] M. Meyer, Une caracterisation volumique de certains espaces normes de dimension finie. Israel J. Math. 55 (1986), 317-326. MR0876398 (88f:52017)

[7] M. Meyer, Convex bodies with minimal volume product in R2. Monatsh. Math. 112 (1991), 297-301. MR1141097 (92k:52015)

[8] M. Meyer and A. Pajor, On Santalo´ inequality. Geometric aspects of functional analysis (1987-88), Lecture Notes in Math., 1376, Springer, Berlin, (1989), 261-263. MR1008727 (90h:52012)

[9] C. M. Petty, Affine isoperimetric problems. Discrete geometry and convexity (New York, 1982), 113-127, Ann. New York Acad. Sci., 440, New York Acad. Sci., New York, 1985. MR0809198 (87a:52014)

[10] S. Reisner, Zonoids with minimal volume-product. Math. Zeitschrift 192 (1986), 339-346. MR0958082 (89i:52015)

[11] S. Reisner, Minimal volume product in Banach spaces with a 1- unconditional basis. J. London Math. Soc. 36 (1987), 126-136. MR0897680 (88h:46029)

[12] J. Saint Raymond, Sur le volume des corps convexes sym etriques. Seminaire d'initiation al Analyse, 1980/1981, Publ. Math. Univ. Pierre et Marie Curie, Paris, 1981. MR0670798 (84j:46033)

[13] L. A. Santalo, An affine invariant for convex bodies of n-dimensional space. (Spanish) Portugaliae Math. 8 (1949), 155-161. MR0039293 (12,526f)

[14] R. Schneider, Convex Bodies: The Brunn-Minkowski Theory. Encyclopedia Math. Appl., vol. 44, Cambridge University Press, Cambridge, 1993. MR1216521, Zbl 0798.52001

Any information missing or wrong?Report an Issue