Volume 162 Issue 1 – July 2005

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

| From volume 162-1

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

Pages 1-64 by Massimo Bertolini, Henri Darmon | From volume 162-1

## Stable ergodicity of certain linear automorphisms of the torus

Pages 65-107 by Federico Rodriguez Hertz | From volume 162-1

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

Pages 109-194 by Hans Lindblad | From volume 162-1

## Geometrization of 3-dimensional orbifolds

Pages 195-290 by Michel Boileau, Bernhard Leeb, Joan Porti | From volume 162-1

## Sharp local well-posedness results for the nonlinear wave equation

Pages 291-366 by Hart F. Smith, Daniel Tataru | From volume 162-1

## Universal bounds for hyperbolic Dehn surgery

Pages 367-421 by Craig Hodgson, Steven P. Kerckhoff | From volume 162-1

## The diameter of the isomorphism class of a Banach space

Pages 423-437 by W. B. Johnson, Edward Odell | From volume 162-1

## On the hardness of approximating vertex cover

Pages 439-485 by Irit Dinur, Samuel Safra | From volume 162-1

## The Schrödinger propagator for scattering metrics

Pages 487-523 by Andrew Hassell, Jared Wunsch | From volume 162-1

## The perimeter inequality under Steiner symmetrization: Cases of equality

Pages 525-555 by Miroslav Chlebík, Andrea Cianchi, Nicola Fusco | From volume 162-1

## Einstein metrics on spheres

Pages 557-580 by Charles P. Boyer, Krzysztof Galicki, János Kollár | From volume 162-1