Volume 162 Issue 1 – July 2005

This issue of the Annals of Mathematics is dedicated to Armand Borel, 1923–2003.

Iwasawa’s Main Conjecture for elliptic curves over anticyclotomic $\Bbb Z_p$-extensions

Pages 1-64 by Massimo Bertolini, Henri Darmon

Stable ergodicity of certain linear automorphisms of the torus

Pages 65-107 by Federico Rodriguez Hertz

Well-posedness for the motion of an incompressible liquid with free surface boundary

Pages 109-194 by Hans Lindblad

Geometrization of 3-dimensional orbifolds

Pages 195-290 by Michel Boileau, Bernhard Leeb, Joan Porti

Sharp local well-posedness results for the nonlinear wave equation

Pages 291-366 by Hart F. Smith, Daniel Tataru

Universal bounds for hyperbolic Dehn surgery

Pages 367-421 by Craig Hodgson, Steven P. Kerckhoff

The diameter of the isomorphism class of a Banach space

Pages 423-437 by W. B. Johnson, Edward Odell

On the hardness of approximating vertex cover

Pages 439-485 by Irit Dinur, Samuel Safra

The Schrödinger propagator for scattering metrics

Pages 487-523 by Andrew Hassell, Jared Wunsch

The perimeter inequality under Steiner symmetrization: Cases of equality

Pages 525-555 by Miroslav Chlebík, Andrea Cianchi, Nicola Fusco

Einstein metrics on spheres

Pages 557-580 by Charles P. Boyer, Krzysztof Galicki, János Kollár