Manuscript XI-F@2 · XI-F-v2.tex · corollary · f4899be0

Corollary: Plateau sum

F3: the plateau sum › The cubic-completed second coefficient · lines 1175–1196 · proof included or linked

XI-F@2#cor:plateau, XI-F@2#eq:plateausum, XI-F@2#eq:plateauzero

If $A γ = 0$ on $U$ , then

A_{2}^{(3)} [γ + K ξ; ϕ_{0}] - A_{2}^{(3)} [γ; ϕ_{0}] = A_{1} [K ζ_{gf} [s_{ξ}]; ϕ_{0}],

a pure switching term of the form (eq:switch), and

A_{2}^{(3)} [γ + K ξ; ϕ_{0}] = A_{2}^{(3)} [γ; ϕ_{0}] whenever D_{f} \cap J^{+} (supp ξ) \subset P_{g} .

Proof. Theorem thm:F3, Proposition prop:gfprops(b), and Lemma lem:switch: $supp ζ_{gf} [s_{ξ}] \subset J^{+} (supp ξ) \cap M_{T} \subset {t \geq ε}$ , with zero data.

Displayed formulas in this passage

XI-F@2#eq:plateausum · line 1178
$A_{2}^{(3)} [γ + K ξ; ϕ_{0}] - A_{2}^{(3)} [γ; ϕ_{0}] = A_{1} [K ζ_{gf} [s_{ξ}]; ϕ_{0}],$
XI-F@2#eq:plateauzero · line 1184
$A_{2}^{(3)} [γ + K ξ; ϕ_{0}] = A_{2}^{(3)} [γ; ϕ_{0}] whenever D_{f} \cap J^{+} (supp ξ) \subset P_{g} .$

Corollary: Plateau sum

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