Index A Aleksandrov solution (of Monge-Amp` ere equa- tion), 129, 136 Aleksandrov’s differentiability theorem, 58 Aleksandrov’s lemma, 84 Aleksandrov-Fenchel inequalities, 192 Alesker-Dar-Milman diffeomorphism, 191 approximate geodesics, 117 arithmetic-geometric inequality, 156 Arnold’s interpretation (Euler equation), 115 Aronson-B´ enilan inequalities, 303 Aronsson’s minimal Lipschitz extension prob- lem, 102 Ascoli’s theorem, 19 B Bakry-Emery theorem, 280, 290 strategy, 275, 289 with skew-symmetric perturbation, 329 Barenblatt-Pattle profile, 301 Barthe inequalities, 196 Beckner-Hirschman uncertainty principle, 286 Bellman principle, 175 Benamou-Brenier formula, 239 Biot-Savart formula, 255 Birkhoff’s theorem, 5, 15 Blachman-Stam inequality, 285 Bochner formula, 178 Boltzmann equation, 223 Borel probability measure, 18 bounded Lipschitz distance, 207 Brascamp-Lieb inequalities, 195 reverse, 196 Brenier map, 67, 85 Brenier solution (Monge-Amp` ere), 130 Brenier’s polar factorization theorem, 109 Brenier’s theorem, 66, 83, 85 Brunn-Minkowski inequality, 184 Burgers’ equation, 170 C Caffarelli’s log concave perturbation theo- rem, 291, 335 center of mass, 153 central limit theorem, 222 change of variable, 9, 125 chaos (for particle systems), 341 characteristics (for transport equations), 166 Choquet’s theorem, 5, 14 concavity, 60 c-concavity, 33, 86 semi-concavity, 91 concentration of measure, 287, 292, 342 conservation of mass, 167 convergence to equilibrium, 288 convexity, 23, 52 in Ê n , 52 semi-convexity, 59 strict convexity, 52 uniform convexity, 59 cost (transportation), 1 homogeneous, 147 optimal, 3 total, 3 Csisz´ar-Kullback-Pinsker inequality, 271, 293 Cullen’s stability principle, 325 cyclical monotonicity, 79, 80, 82, 88 c-cyclical monotonicity, 86 367

Purchased from American Mathematical Society for the exclusive use of nofirst nolast (email unknown) Copyright 2003 American Mathematical Society. Duplication prohibited. Please report unauthorized use to cust-serv@ams.org. Thank You! Your purchase supports the AMS' mission, programs, and services for the mathematical community.