The Flatness Theorem for Nonsymmetric Convex Bodies via the Local Theory of Banach Spaces
Published Online:1 Aug 1999https://doi.org/10.1287/moor.24.3.728
References
- Inequalities for convex bodies and polar reciprocal lattices in ℝ n II: Application of K-convexity. Discrete Comput. Geom. (1996) 16 305 311 Crossref, Google Scholar
- An extremal property of the mean width of the simplex. Math. Ann. (1998a) 310 685 693 Crossref, Google Scholar
- On a reverse form of the Brascamp-Lieb inequality. Invent. Math. (1998b) 134 335 361 Crossref, Google Scholar
- Random factorization of operators between Banach spaces. J. Analyse Math. (1981) 39 45 74 Crossref, Google Scholar
- On martingale transforms in finite dimensional lattices with an appendix on the K-convexity constant. Math. Nachr. (1984) 119 41 53 Crossref, Google Scholar
- Distances between normed spaces, their subspaces and quotient spaces. Integral Equations Operator Theory (1986) 9 31 46 Crossref, Google Scholar
- New volume ratio properties for convex symmetric bodies in R n . Invent. Math. (1987) 88 319 340 Crossref, Google Scholar
- Best constants in Young's inequality, its converse and its generalization to more than three functions. Adv. Math. (1976) 20 151 173 Crossref, Google Scholar
- Projections onto Hilbertian subspaces of Banach spaces. Israel J. Math. (1979) 33 155 171 Crossref, Google Scholar
- , Gruber P. M. , Wills J. M. Lattice points. Handbook of Convex Geometry (1993) (North-Holland, Amsterdam) 765 797 Google Scholar
- Measures of symmetry for convex sets. Proc. Sympos. Pure Math. 7 (1963) (Amer. Math. Soc., Providence, RI) 233 270 Google Scholar
- Extremum problems with inequalities as subsidiary conditions. Courant Anniversary Volume (1948) (Interscience, New York) 187 204 Google Scholar
- Covering minima and lattice-point-free convex bodies. Ann. Math. (1988) 128 577 602 Crossref, Google Scholar
- On the Width of Lattice-Free Simplices (1998) . (Preprint) Google Scholar
- A quantitative formulation of Kronecker's theory of approximation. Izv. Acad. Nauk SSSR (1948) 12 113 122 . Ser. Mat. (in Russian) Google Scholar
- Integer programming with a fixed number of variables. Math. Oper. Res. (1983) 8 538 548 Link, Google Scholar
- Ellipsoids defined by Banach ideal norms. Mathematika (1979) 26 1 18 29 Crossref, Google Scholar
- , Gruber P. M. , Wills J. M. The local theory of normed spaces and its applications to convexity. Handbook of Convex Geometry (1993) (North-Holland, Amsterdam) 1149 1220 Google Scholar
- Private communication. (1998) Google Scholar
- Asymptotic Theory of Finite Dimensional Normed Spaces (1986) 1200 (Springer-Verlag, Berlin–New York) . Lecture Notes in Math. Google Scholar
- , Lacey E. H. Geometry of finite-dimensional Banach spaces and operator ideals. Notes in Banach Spaces (1980) (University of Texas Press, Austin, TX) 81 181 Google Scholar
- , Lin B.-L. K-convexity. Proc. Res. Workshop Banach spaces operator ideals (1981) (University of Iowa, Iowa City, IA) 139 151 Google Scholar
- Probabilistic methods in the geometry of Banach spaces. C.I.M.E. Varenna 1985 (1986) 1206 (Springer Verlag, Berlin–New York) 167 241 . Lecture Notes in Math. Google Scholar
- The Volume of Convex Bodies and Banach Space Geometry (1989) (Cambridge University Press, Cambridge) Crossref, Google Scholar
- Distances between nonsymmetric convex bodies and the MM *-estimate. (1998) . Preprint. Available at http://xxx.lanl.gov/abs/math/9812010 Google Scholar
- An Introduction to Empty Lattice Simplices (1998) (Springer Verlag) . IPCO 7, Lecture Notes in Computer Science, (to appear) Google Scholar
- Regularity of Gaussian measures. Acta Math. (1987) 159 99 149 Crossref, Google Scholar
- Covering the lattice points of a convex body with affine subspaces. Intuitive Geometry (Budapest, 1995) (1997) >429 440 . Bolyai Soc. Math. Stud., 6, Janos Bolyai Math. Soc., Budapest, 1997 Google Scholar
- Banach-Mazur Distances and Finite-Dimensional Operator Ideals (1989) (Longman Scientific & Technical, Harlow) . Pitman Monographs and Surveys in Pure and Applied Mathematics, 38. copublished in the United States with John Wiley & Sons, Inc., New York Google Scholar

