Manuscript VII-A-ST@1 · VII-A-ST.tex · definition · c39a67a3

Definition: Plateau and restricted gauge data

Switching before variation · lines 495–517

VII-A-ST@1#def:plateau, VII-A-ST@1#eq:formal-group

Fix

g \in C_{c}^{\infty} (D_{+}^{\circ}), 0 \leq g \leq 1, U \subset int {g = 1} .

The test is real $f \in C_{c}^{\infty} (U)$ . Let

g_{U} = C_{c}^{\infty} (U; T D) .

The admitted formal transformations are

F_{κ}^{*} = exp (κ L_{ξ} + κ^{2} L_{ζ}) (mod κ^{3}), ξ, ζ \in g_{U} .

They are formal jets of orientation-preserving diffeomorphisms generated inside $U$ . Their group is denoted $G_{U}$ .

Displayed formulas in this passage

VII-A-ST@1#eq:formal-group · line 509
$F_{κ}^{*} = exp (κ L_{ξ} + κ^{2} L_{ζ}) (mod κ^{3}), ξ, ζ \in g_{U} .$
unlabeled · line 498
$g \in C_{c}^{\infty} (D_{+}^{\circ}), 0 \leq g \leq 1, U \subset int {g = 1} .$
unlabeled · line 505
$g_{U} = C_{c}^{\infty} (U; T D) .$