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 59, Number 1

#### Publication Date: August 1989

Heights for local systems on curves

Jean-Luc Brylinski; 1-26

Trace formula for compact $\Gamma\setminus PSL_{2}(\mathbb{R})$ and the equidistribution theory of closed geodesics

Steven Zelditch; 27-81

Generic Torelli theorem for hypersurfaces of certain compact homogeneous Kähler manifolds

Kazuhiro Konno; 83-160

Remarques sur le probleme exterieur de Plateau

Romain Krust; 161-173

Distinguished cusp forms are theta series

Jian-Shu Li; 175-189

Wiener’s criterion for divergence form parabolic operators with $C^1$-Dini continuous coefficients

Eugene B. Fabes, Nicola Garofalo and Ermanno Lanconelli; 191-232

The infinitesimal Abel-Jacobi mapping and moving the $\mathcal{O}(2) + \mathcal{O}(-4)$ curve

Herbert Clemens; 233-240

The rank condition and convergence of formal functions

Shuzo Izumi; 241-264

Semirigid partial differential operators and microlocal analytic hypoellipticity

A. Alexandrou Himonas; 265-287

On isospectral locally symmetric spaces and a theorem of von Neumann

R. J. Spatzier; 289-294

On a conjecture of Barry Simon on trace ideals

Fernando Cobos and Thomas Kühn; 295-299

Dimension of holomorphic extensions of complex spaces

Sandra Hayes and Geneviève Pourcin; 301-309