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