Manuscript IX-E-3@1 · IX-E-3.tex · proposition · 8c41417a

Proposition: Exact support of the local quadratic slot

Derivative support and surface non-cancellation · lines 453–465 · proof included or linked

IX-E-3@1#eq:Wexact

For every $g$ ,

supp_{fun} W_{g} = G .

Proof. At the allowed configuration $h_{00} = 1$ , the metric derivative has kernel $2 g$ , whose support is $G$ ; combine this with the upper bound in (eq:upper).

Displayed formulas in this passage

IX-E-3@1#eq:Wexact · line 455
$supp_{fun} W_{g} = G .$

Nearby in this section

section: Derivative support and surface non-cancellation
lemma: Lemma: Injectivity of the surface coefficient
lemma: Lemma: A smooth surface coefficient cannot be cancelled
section: Derivative support and surface non-cancellation