Includes bibliographical references.

Some recent developments in Riemannian geometry ; Designer metrics on Riemannian manifolds ; Open manifolds of nonnegative curvature ; An extrinsic average variational method ; The Dirichlet problem and Fatou's theorem for harmonic mappings on regular domains ; New examples of singlyperiodic minimal surfaces and their qualitative behavior ; The Gauss curvature and Minkowski problems in space forms ; Selfduality, twistor theory, its generalization and application ; Spectral geometry of Riemannian manifolds ; Eigenvalue asymptotics and their geometric applications ; A lower bound for the number of isospectral surfaces ; The conformal deformation equation and isospectral set of conformal metrics ; Analytic torsion for group actions ; Regularity of entropy for geodesic flows ; Twistor and Gauss lifts of surfaces in fourmanifolds ; Affine differential geometry of complex hypersurfaces ; Domains with noncompact automorphism groups ; Affine approach to complex geometry ; Compactification of complete KahlerEinstein manifolds of finite volume ; Topological type of isolated hypersurface singularities ; Complex foliations Robert E Greene ; Robert Brooks ; Gerard Walschap ; S Walter Wei ; Patricio Aviles ; David A Hoffman ; Vladimir I Oliker ; Y Sun Poon ; Peter B Gilkey ; Mark A Pinsky ; Richard M Tse ; SunYung A Chang and Paul C Yang ; John Lott ; G Knieper and H Weiss ; Gary R Jensen and Marco Rigoli ; Weiqi Gao ; KangTae Kim ; Sidney Frankel ; Ngaiming Mok ; Stephen ST Yau ; T Duchamp and M Kalka