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Notation Index

(BCP), 110

(BCPB), 155

(BCPS), 216

(CL), 212

(CP), 112

(CP i), 217

(CP ii), 217

(CPS), 217

(F1), 109

(F2), 109

(F3



), 109

(F3), 109

(F4), 110

(f1), 163

(f2), 164

(I), 212

(SP), 212

a ∧ b,49

a ∨ b,94

↑ a, 174

(z), 70

BUC, 139

,15

2m,m

,18

(O), 72

d(x, A), 182

d(z,S), 85

dist(x, A), 182

dist(A, B), 217

E,40

F,77

∗

,50

∗

,50

I,24

(Z), 165

lim, 51

lim

, 124

lim inf

ε→0

∗

,75

lim sup

ε→0

∗

,75

Limsup

j→∞

,85

n,17

∇u,8

∇

u,8

∇n,32

|p|,17

O,43

(X), 27

,27

,35

spt, 178

N−1

,26

,32

⊗,23

trace, 23

|X|,50

X>O,46

X ≥ Y ,43

Y 

,46

Subject Index

ε-core, 184

ε-neighborhood, 184

aﬃne curvature ﬂow equation, 35

anisotropic, 26

barrier subsolution, 231

barrier supersolution, 226

Cahn–Hoﬀman vector, 26

closed evolution, 166

compatible, 77

curvature shortening equation, 34

degenerate elliptic, 42, 45, 69

degenerate parabolic, 45, 48

distance, 182

elementary symmetric polynomial,

evolving hypersurface, 18

Frank diagram, 61

Gaussian curvature, 25

Gaussian curvature ﬂow equation, 34

geometric, 46, 48

graph representation, 16

harmonic curvature, 25

harmonic curvature ﬂow equation, 35

Hausdorﬀ distance, 185

indicator function, 55

interface evolution, 166

left accessible, 119

level set equation, 37

level set mean curvature ﬂow equa-

tion, 38

level set representation, 16

level set solution, 224

level set subsolution, 221

lower relaxed limit, 75

lower semicontinuous, 70

lower semicontinuous envelope, 50,

lower test function, 72

mean curvature, 24, 26

mean curvature ﬂow equation, 34

mean curvature vector, 25

Minkowski function, 55

mobility, 33

modulus, 80

normal curvature, 22

normal velocity, 18

open evolution, 165

orientation, 17

orientation-free, 171

outward, 18

parabolic boundary, 73

parabolic subjet, 115

parabolic superjet, 115

parametric representation, 16

positively homogeneous of degree 1,

principal curvatures, 22

second fundamental form, 21, 23

264 Subject Index

self-similar, 53

set-theoretic solution, 208

set-theoretic subsolution, 208, 211

signed distance function, 182

solution, 72

strictly elliptic, 45

strictly parabolic, 46

strongly geometric, 40

subjet, 114

subsolution, 71, 78, 93

superjet, 113

supersolution, 71, 78, 93

symmetric curvature, 25

symmetric curvature ﬂow equation,

tangent space, 16

tangent vector, 16

uniformly upper semicontinuous, 218

unit normal vector, 17

unit normal vector ﬁeld, 17

upper relaxed limit, 75, 85

upper semicontinuous, 71

upper semicontinuous envelope, 50,

upper test function, 72

Weingarten map, 21

Wulﬀ shape, 54