Manuscript XII-E@1 · XII-E.tex · theorem · 9471ea56

Theorem: Exact assembled plateau variation

E3: the ledger, printed before addition › The rows · lines 782–800 · proof included or linked

XII-E@1#thm:assembly, XII-E@1#eq:assembly

For $ξ \in g_{U}$ and $P_{m} ϕ = 0$ ,

Δ_{ξ} Φ^{(2)}_{D} = - A_{1} [f, g] (K ρ_{ξ} [γ]; ϕ) + A_{1} [f, g] (e_{ξ} [γ]; ϕ) .

Proof. By (eq:PhiD) and Lemma lem:affine, $Δ_{ξ} Φ^{(2)}_{D} = [A_{2}^{sc} (γ + K ξ, r_{D} [γ]; ϕ) - A_{2}^{sc} (γ, r_{D} [γ]; ϕ)] + A_{1} (r_{D} [γ + K ξ] - r_{D} [γ]; ϕ)$ . The bracket is Lemma lem:heldfixed with $k = r_{D} [γ]$ ; the second term is Lemma lem:DeltarD. Add.

Displayed formulas in this passage

XII-E@1#eq:assembly · line 785
$Δ_{ξ} Φ^{(2)}_{D} = - A_{1} [f, g] (K ρ_{ξ} [γ]; ϕ) + A_{1} [f, g] (e_{ξ} [γ]; ϕ) .$

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section: The rows