theorem A.492 Douglas' conformality theorem; quoted

open in the book · appendices/A-long-proofs.tex:24113 · p. 3033

Rests on

depends_on definition A.481 Douglas' boundary functional ¶
- 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 13.18 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 ¶
depends_on lemma A.487 The normalisation costs nothing ¶
- depends_on lemma A.479 Conformal invariance of the Dirichlet integral ¶
  - depends_on definition A.476 Disc-type surfaces and the two functionals ¶ ↺
  - depends_on proposition 7.31 Chain rule ¶
    - depends_on definition 7.13 Composite function ¶
      - depends_on definition 7.9 Real function ¶
    - depends_on proposition 7.27 Differentiable implies continuous ¶
      - depends_on definition 7.20 Continuity at a point ¶
      - depends_on definition 7.26 Derivative of a function at a point ¶
      - depends_on proposition 7.6 Algebra of limits ¶
      - proves proof ch:05-real-analysis@proof-11 ¶
    - depends_on proposition 7.6 Algebra of limits ¶ ↺
    - proves proof ch:05-real-analysis@proof-15 ¶
  - proves proof app:A-long-proofs@proof-284 ¶
- depends_on lemma A.485 Conformal automorphisms of the disc ¶
  - depends_on lemma A.479 Conformal invariance of the Dirichlet integral ¶ ↺
  - proves proof app:A-long-proofs@proof-287 ¶
- proves proof app:A-long-proofs@proof-288 ¶

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type	direction	node	provenance	where
`cites` (history)	→	Solution of the problem of Plateau	derived	appendices/A-long-proofs.tex:24128
`depends_on`	→	Douglas' boundary functional	declared	appendices/A-long-proofs.tex:24129
`depends_on`	→	The normalisation costs nothing	declared	appendices/A-long-proofs.tex:24129