Math 1500 (Analytic Geometry and Calculus I)

**Books.**

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)**

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

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

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

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

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

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