Index absorbing inequality, 48, 93 Allard regularity theorem, 105, 119 almost conformal, 135, 191 almost maximal, 175 almost stable, 92 almost stable sectors, 268, 271 alternating method, 176 area estimate for stable surfaces, 77 aspherical, 255 asymptotically flat, 251 barrier, 140 Barta’s theorem, 46, 48 bent helicoids, 59 Bernstein’s theorem, 32, 48, 50, 78, 88, 101, 103 Bers’ theorem, 208, 237 Birkhoff’s curve shortening, 165 Bochner formula, 61, 99, 150, 242 branch point, 147 false, 215 true, 215 bubble compactness, 179 bubble convergence, 128 Calabi’s more ambitious conjecture, 283 Calabi-Yau conjectures, 283 calculus of variations direct method, 141 calibration, 3, 119 catenoid, 9, 34 Cauchy-Riemann equations, 34 Chen-Gackstatter surface, 17 Choi-Schoen theorem, 244 Choi-Wang theorem, 244, 245 chord-arc, 74, 287 assuming bounded curvature, 287 Christoffel symbols, 235 CLP surface, 20 coarea formula, 24 Codazzi equation, 67 cone, 101 conformal map, 143 metric, 144 conformal dilation, 128 conjugate minimal surface, 35 convex hull property, 23 convexity theorem for harmonic maps, 177 Costa-Hoffman-Meeks surface, 14 Courant-Lebesgue lemma, 143 covering lemma five times, 115 critical set, 207 curvature Riemann, 66 curvature estimate embedded disks, 82, 83 graphs, 73, 88 small excess, 80 small total curvature, 72 stable, 78 Dirichlet problem, 137 311

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