Manuscript IX-D-ST@1 · IX-D-ST.tex · proposition · b1dc631a

Proposition: Exact support of the quadratic slot

Exact quadratic support and surface non-cancellation · lines 1718–1733 · proof included or linked

IX-D-ST@1#prop:Wexact, IX-D-ST@1#eq:Wexact

For every test $g$ ,

supp_{fun} W_{g} = supp g .

Proof. The upper inclusion is immediate. At the allowed configuration $h_{00} = 1$ , the metric derivative is $2 g$ in the $00$ -component. Its distributional support is $supp g$ . Lemma lem:derivativesupport gives the lower inclusion.

Displayed formulas in this passage

IX-D-ST@1#eq:Wexact · line 1721
$supp_{fun} W_{g} = supp g .$

Nearby in this section

section: Exact quadratic support and surface non-cancellation
lemma: Lemma: Injective surface coefficient
lemma: Lemma: A bounded bulk term cannot cancel a surface delta
section: Exact quadratic support and surface non-cancellation