Manuscript X-I-ST@1 · X-I-ST.tex · section · 9745fd40

Plateau and the additional compact vertex

The unchanged host and the support contract › Plateau and the additional compact vertex · lines 336–365

X-I-ST@1#eq:a

Retain the smooth compact scalar switch $g$ , the observation test $f$ , the open plateau $U$ , and the onset

σ_{ε} (t) = χ (t / ε), 0 < ε < δ,

where $χ$ is smooth, zero for arguments at most zero, and one for arguments at least one. Assume

U ⋐ L, g = σ_{ε} = 1 on a neighborhood of U .

The relative compact gauge parameters are

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

Choose once and for all

a \in C_{c}^{\infty} (U; R), a \geq 0, a \neq \equiv 0.

This is a new coupling profile, not a new regulator. Its support is inside the already retained plateau and therefore requires no enlarged host chart or smaller width.

Displayed formulas in this passage

X-I-ST@1#eq:a · line 358
$a \in C_{c}^{\infty} (U; R), a \geq 0, a \neq \equiv 0.$
unlabeled · line 340
$σ_{ε} (t) = χ (t / ε), 0 < ε < δ,$
unlabeled · line 347
$U ⋐ L, g = σ_{ε} = 1 on a neighborhood of U .$
unlabeled · line 353
$g_{U} = C_{c}^{\infty} (U; T M) .$

Plateau and the additional compact vertex

Displayed formulas in this passage

Nearby in this section