The author is indebted to Yves Benoist, Laurent Clozel, Patrick Gérard, François Labourie, Gilles Lebeau, Yves Le Jan, Werner Müller, and Yuri Tschinkel for very helpful discussions and remarks. I am especially grateful to Gilles Lebeau for many heated, fruitful, if nonacademic, discussions. Without his support, this work would not have been completed. I am also indebted to Xiaonan Ma and Weiping Zhang for their critical comments. Finally, I thank Courant Institute and New York University for supporting my stay during the spring terms of 2007, 2008, and 2009.