proposition A.478 $D\ge A$, with equality exactly for conformal maps

open in the book · appendices/A-long-proofs.tex:23511 · p. 3028

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 ¶
proves proof app:A-long-proofs@proof-283 ¶

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type	direction	node	provenance	where
`depends_on`	→	Disc-type surfaces and the two functionals	declared	appendices/A-long-proofs.tex:23516
`proves`	←	app:A-long-proofs@proof-283	declared	appendices/A-long-proofs.tex:23519