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 52, Number 1

#### Publication Date: March 1985

The diffusion approximation of the spatially homogeneous Boltzmann equation

On the not integrally closed subrings of the ring of the thetanullwerte

Riccardo Salvati Manni; 25-33

Front d’onde analytique et sommes de carres de champs de vecteurs

A. Grigis and J. Sjöstrand; 35-51

Symmetry of constant mean curvature hypersurfaces in hyperbolic space

Gilbert Levitt and Harold Rosenberg; 53-59

Pluri-canonical divisors on Kähler manifolds II

Marc Levine; 61-65

CR extension near a point of higher type

A. Boggess and J. Pitts; 67-102

Lifting problems and local reflexivity for $C^\ast$-algebras

Edward G. Effros and Uffe Haagerup; 103-128

Blowings-up of $\mathbf{P}^2$ and their blowings-down

Brian Harbourne; 129-148

The invariants of the Tate-Shafarevich group in a $\mathbf{Z}_p$-extension can be infinite

Gudrun Brattström; 149-156

Quelques problemes de prolongement de courants en analyse complexe

Nessim Sibony; 157-197

Le probleme de Dirichlet pour l’operateur de Schrodinger

Jean Brossard; 199-210

On the spectrum of the Hecke groups

R. S. Phillips and P. Sarnak; 211-221

Lie groups and twistor spaces

Robert L. Bryant; 223-261

The dimension of smoothing components

G.-M. Greuel and E. Looijenga; 263-272

Relative vanishing theorems in analytic spaces

Kensho Takegoshi; 273-279