definition A.481 Douglas' boundary functional

open in the book · appendices/A-long-proofs.tex:23605 · p. 3029

ground object -- no derivation owed

Rests on

depends_on definition A.476 Disc-type surfaces and the two functionals ¶
- depends_on definition 13.22 First fundamental coefficients ¶
  - depends_on definition 13.21 First fundamental form ¶
    - depends_on definition 13.11 Arc length ¶
      - depends_on definition 13.8 Curve ¶
      - depends_on definition 13.9 Tangent vector to a curve ¶
    - depends_on definition 13.18 Surface ¶
  - depends_on definition 13.19 Parameter curves ¶
    - depends_on definition 13.8 Curve ¶ ↺
    - depends_on definition 13.18 Surface ¶ ↺
- depends_on equation 16.60 eq:calcvar-dirichlet-integral ¶

Supports

depends_on definition A.486 The normalised admissible class ¶
depends_on lemma A.484 Lower semicontinuity of the Douglas functional ¶
depends_on theorem A.492 Douglas' conformality theorem; quoted ¶
depends_on theorem A.482 Douglas' identity ¶

Neighborhood

Every logical edge within two steps of this node.

declared and complete
partly declared
a check failed
not graded
declared in the source
inferred from structure

Edges

type	direction	node	provenance	where
`depends_on`	→	Disc-type surfaces and the two functionals	declared	appendices/A-long-proofs.tex:23617
`depends_on`	←	The normalised admissible class	declared	appendices/A-long-proofs.tex:23873
`depends_on`	←	Lower semicontinuity of the Douglas functional	declared	appendices/A-long-proofs.tex:23764
`depends_on`	←	Douglas' conformality theorem; quoted	declared	appendices/A-long-proofs.tex:24129
`depends_on`	←	Douglas' identity	declared	appendices/A-long-proofs.tex:23637