Published by Duke University Press since its inception in 1935, the Duke Mathematical Journal is one of the world's leading mathematical journals. Without specializing in a small number of subject areas, it emphasizes the most active and influential areas of current mathematics.

### Volume 71, Number 1

#### Publication Date: July 1993

The Cauchy problem for the Korteweg-de Vries equation in Sobolev spaces of negative indices

Carlos E. Kenig, Gustavo Ponce and Luis Vega; 1-21

A complete minimal Klein bottle in $\mathbb{R}^3$

Francisco J. López; 23-30

On the asymptotic behavior of spherically symmetric wave maps

Demetrios Christodoulou and A. Shadi Tahvildar-Zadeh; 31-69

Splitting of nonnegatively curved leaves in minimal sets of foliations

Scot Adams and Garrett Stuck; 71-92

Centrally trivial automorphisms and an analogue of Connes’s $\chi(M)$ for subfactors

Yasuyuki Kawahigashi; 93-118

Singularities of the solution to a certain Cauchy problem and an application to the Pompeiu problem

Peter Ebenfelt; 119-142

Density of integer points on affine homogeneous varieties

W. Duke, Z. Rudnick and P. Sarnak; 143-179

Mixing, counting, and equidistribution in Lie groups

Alex Eskin and Curt McMullen; 181-209

Asymptotics of the determinant of the Laplacian on hyperbolic surfaces of finite volume

Rolf E. Lundelius; 211-242

Asymptotic completeness for $N \leq 4$ particle systems with the Coulomb-type interactions

I. M. Sigal and A. Soffer; 243-298

Rational and real homotopy theory with arbitrary fundamental groups

Edgar H. Brown, Jr. and Robert H. Szczarba; 299-316

When is a family of submanifolds locally diffeomorphic to a family of planes?

A. B. Goncharov; 317-331

Addendum to: “A perturbation result in prescribing scalar curvature on $S^n$”

Sun-Yung Alice Chang and Paul C. Yang; 333-335