proposition A.493 A harmonic conformal map is a minimal surface

open in the book · appendices/A-long-proofs.tex:24132 · p. 3033

Rests on

depends_on definition 13.25 Second fundamental coefficients ¶
- depends_on definition 13.24 Second fundamental form ¶
  - depends_on definition 13.20 Unit normal vector of a surface ¶
    - depends_on definition 13.19 Parameter curves ¶
      - depends_on definition 13.8 Curve ¶
      - depends_on definition 13.18 Surface ¶
- depends_on definition 13.20 Unit normal vector of a surface ¶ ↺
depends_on proposition 16.8 The minimal-surface equation ¶
- depends_on equation 16.6 eq:calcvar-area-functional ¶
- depends_on equation 16.32 eq:calcvar-euler-lagrange-field ¶
- proves proof ch:14-calculus-of-variations@proof-4 ¶
proves proof app:A-long-proofs@proof-292 ¶

Nothing declares a dependency on this node yet.

Every logical edge within two steps of this node.

type	direction	node	provenance	where
`depends_on`	→	Second fundamental coefficients	declared	appendices/A-long-proofs.tex:24139
`depends_on`	→	The minimal-surface equation	declared	appendices/A-long-proofs.tex:24139
`proves`	←	app:A-long-proofs@proof-292	declared	appendices/A-long-proofs.tex:24143