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 53, Number 4

#### Publication Date: December 1986

Structure of positive solutions to $(-\Delta+V)u=0$ in $R^n$

Minoru Murata; 869-943

Propagation des singularites pour des operateurs pseudo-differentiels a symboles reels

Bernard Lascar and Richard Lascar; 945-981

The Cauchy problem for semilinear hyperbolic systems with discontinuous data

Guy Metivier; 983-1011

Unitary representations of the Virasoro algebra

Akihiro Tsuchiya and Yukihiro Kanie; 1013-1046

Some Euler products associated with cubic metaplectic forms on $\mathrm {GL}(3)$

Daniel Bump and Jeffrey Hoffstein; 1047-1072

Topology of real algebraic threefolds

Wojciech Kucharz; 1073-1079

Eichler-Shimura homology and the finite generation of cusp forms by hyperbolic Poincaré series

William M. Goldman and John J. Millson; 1081-1091

Duality theorems for Néron models

William G. McCallum; 1093-1124

A note on Kollár’s theorem

Donu Arapura; 1125-1130

Correction to “On the differentiability of $\mathbf{O}(n)$ invariant functions of symmetric matrices,” vol. 52 (1985) pp. 475–484

John Sylvester; 1131-1132