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 50, Number 4

#### Publication Date: December 1983

Characteristics and existence of isometric embeddings

Robert L. Bryant, Phillip A. Griffiths and Deane Yang; 893-994

On Alexandrov-Bernstein theorems in hyperbolic space

Manfredo P. do Carmo and H. Blaine Lawson, Jr.; 995-1003

Remarks on our paper “A scattering theory for time-dependent long-range potentials”

Hitoshi Kitada and Kenji Yajima; 1005-1016

Mixed Hodge structures on punctured neighborhoods

Alan H. Durfee; 1017-1040

Division algebras, fibrations of spheres by great spheres and the topological determination of space by the gross behavior of its geodesics

Herman Gluck, Frank Warner and C. T. Yang; 1041-1076

Algebraically irreducible representations of $L^1$-algebras of exponential Lie groups

Detlev Poguntke; 1077-1106

Abelian and solvable subgroups of the mapping class groups

Joan S. Birman, Alex Lubotzky and John McCarthy; 1107-1120

A symplectic rigidity theorem

Alan Weinstein; 1121-1125

Degenerations of quintic threefolds and their lines

Sheldon Katz; 1127-1135

Theta functions and holomorphic differential forms on compact quotients of bounded symmetric domains

Greg W. Anderson; 1137-1170

Pointwise convergence of singular convolution operators

Allan Greenleaf; 1171-1199

Category$\mathcal{O}^\prime, \mathfrak{n}$-homology and the reducibility of generalized principal series representations

David H. Collingwood; 1201-1224

An isoperimetric inequality with applications to curve shortening

Michael E. Gage; 1225-1229

Calibrations on $\mathbf{R}^6$

Jiri Dadok and Reese Harvey; 1231-1243

Commensurability of co-compact three-dimensional hyperbolic groups

A. M. Macbeath; 1245-1253

On the essential selfadjointness of stochastic Schrödinger operators

Werner Kirsch and Fabio Martinelli; 1255-1260

A discrete stochastic integral inequality and balanced random walk in a random environment

Gregory F. Lawler; 1261-1274