Alexander Koldobsky's Home Page

Curriculum Vitae

Math 1500 (Analytic Geometry and Calculus I)


Fourier Analysis in Convex Geometry, Mathematical Surveys and Monographs, American Mathematical Society, Providence RI 2005. Available at

The Interface between Convex Geometry and Harmonic Analysis, CBMS Regional Conference Series,
American Mathematical Society, Providence RI, 2008 (with V.Yaskin)

                                                                                                                            Recent papers.

Stability and separation in volume comparison problems, submitted

On the maximal measure of sections of the n-cube, submitted (with H.K\"onig)

Complex intersection bodies, submitted (with G.Paouris and M.Zymonopoulou)

Stability and slicing inequalities for intersection bodies, Geom. Dedicata, to appear (with Dan Ma)

Minimal volume of slabs in the complex cube, Proc. Amer. Math. Soc. 140 (2012), 1709--1717 (with H.K\"onig)

Positive definite functions and stable random vectors, Israel J. Math. 185 (2011), 277--292.

A hyperplane inequality for measures of convex bodies in R^n, n\le 4, Discrete Comput. Geom. 47 (2012), 538--547.

Isomorphic properties of intersection bodies, J. Funct. Anal. 261 (2011), 2697-2716 (with G.Paouris and M.Zymonopoulou)

Stability of volume comparison for complex convex bodies, Arch. Math. 97 (2011), 91--98.

Stability in the Busemann-Petty and Shephard problems, Adv. Math. 228 (2011), 2145--2161.

Stability in volume comparison problems, Max Planck Institute Preprint Series, 2011-18

Volumes of lower-dimensional slabs and sections of the cube, Adv. Appl. Math. 47 (2011), 894--907 (with H.K\"onig)

A note on positive definite norm dependent functions, in High Dimensional Probability V: The Luminy Volume,
Institute of Mathematical
Statistics Collections, 2009, 30-36.

The complex Busemann-Petty problem on sections of convex bodies, Adv. Math. 218 (2008), 352-367 (with H.K\"onig and M.Zymonopoulou)

Inequalities of the Kahane-Khinchin type and sections of $L_p$-balls, Studia Math. 184 (2008), 217-231 (with A.Pajor and V.Yaskin)

Determination of convex bodies by derivatives of section functions, Arch. Math. 88 (2007), 279-288 (with C.Shane)

Sobolev spaces with trivial isometries, Positivity 10 (2006), 135-144 (with G.Diestel)

The geometry of L_0, Canad. J. Math. 59 (2007), 1029-1049  (with N.Kalton, V.Yaskin, M.Yaskina)

Intersection bodies and L_p-spaces, Adv. Math. 196 (2005), 257-275 (with N.Kalton)

Modified Busemann-Petty problem on sections of convex bodies , Israel J. Math., to appear (with V.Yaskin and M.Yaskina)

Comparison of volumes by means of areas of central sections, Adv. Appl. Math. 33 (2004), 728-732

Extremal sections of complex $l_p$-balls, $0<p<2$, Studia Mathematica 159 (2003), 185-194 (with M.Zymonopoulou)

Fourier methods in the study of sections and projections of convex bodies, in Fourier Analysis and Convexity, L.Brandolini et al, eds, 119-130 (with D.Ryabogin and A.Zvavitch)

Projections of convex bodies and the Fourier transform, Israel J. Math. 139 (2004), 361-380 (with D.Ryabogin and A.Zvavitch)

Banach spaces embedding isometrically into $L_p$ when $0<p<1$ (with N.Kalton), Proc. Amer. Math. Soc. 132 (2004), 67-76

The Busemann-Petty problem via spherical harmonics, Adv. Math. 177 (2003), 105-114

Extremal slabs in the cube and the Laplace transform (with F.Barthe), Adv. Math. 174 (2003), 89-114

Sections of star bodies and the Fourier transform, Contemp. Math. 320 (2003), 225-248

On the central limit properties of convex bodies (with S.Bobkov), Lect. Notes in Math. 1807 (2003), 44-52

On the derivatives of X-ray functions, Arch. Math. 79 (2002), 216--222.

Aspects of the isometric theory of Banach spaces (with H.Koenig), Handbook of the Geometry of Banach Spaces, Elsevier, 2001, p. 899--939

Average volume of sections of star bodies (with M.Lifshits), Lect. Notes in Math. 1745 (2000), 119--146.

A functional analytic approach to intersection bodies, GAFA 10 (2000), 1507--1526

An analytic solution to the Busemann-Petty problem on sections of convex bodies (with R.J. Gardner and Th. Schlumprecht),Annals of Math. 149 (1999), 691--703

A generalization of the Busemann-Petty problem on sections of convex bodies, Israel J. Math. 110 (1999), 75--91

A short proof of Schoenberg's conjecture on positive definite functions (with Y.Lonke), Bull. London Math. Soc. 31 (1999), 693--699

A correlation inequality for stable random vectors, Contemp. Math. 234 (1999), 121--124

Positive definite distributions and subspaces of $L_{-p}$ with applications to stable processes, Canad. Math. Bull. 42 (1999), 344-353

Intersection bodies, positive definite distributions and the Busemann-Petty problem, Amer. J. Math. 120 (1998), 827--840

Intersection bodies in $R^4$, Adv. Math. 136 (1998), 1--14

Second derivative test for intersection bodies, Adv. Math. 136 (1998), 15--25

An application of the Fourier transform to sections of star bodies, Israel J. Math. 106 (1998), 157--164