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 69, Number 1

#### Publication Date: January 1993

The differential form spectrum of manifolds of positive curvature

Jose F. Escobar and Alexandre Freire; 1-41

The penalized obstacle problem. I. Lipschitz regularity of level sets

Juan C. Redondo; 43-65

The penalized obstacle problem. II. $C^{1,\alpha}$ regularity of level sets

Juan C. Redondo; 67-85

Décomposition du fibré normal des surfaces lisses de $\mathbb{P}_4$ et structures doubles sur les solides de $\mathbb{P}_5$

Bénédicte Basili and Christian Peskine; 87-95

Free products of hyperfinite von Neumann algebras and free dimension

Ken Dykema; 97-119

Singular matrices and a uniform bound for congruence groups of $SL_n(\mathbf{Z})$

Y. R. Katznelson; 121-136

Deux théorèmes de comparaison en cohomologie étale; applications

Bruno Kahn; 137-165

On the decomposition of a representation of $GL(3)$ restricted to $GL(2)$ over a $P$-adic field

Cohomology of quantum groups at roots of unity

Victor Ginzburg and Shrawan Kumar; 179-198

Riemann surfaces and abelian varieties with an automorphism of prime order

Gonzalo Riera and RubÍ E. RodrÍguez; 199-217

The $GL(3)$ Rankin-Selberg convolution for functions not of rapid decay

Daniel B. Lieman; 219-242

Another proof of Sumihiro’s theorem on torus embeddings

Jonathan Fine; 243-245