Manuscript XV-C@1 · XV-C.tex · section · 5afd124d

Local geometric hypotheses

The supported-sector criterion in evaluable form › Local geometric hypotheses · lines 957–983

XV-C@1#eq:puncturedform

Continue in a product normal chart

U = X \times V_{q}, S = X \times {0} .

Let $A \subset U$ be relatively closed and set

Z = {x \in X : (x, 0) \in A} .

Suppose $t^{\circ} \in D^{'} (U ∖ A)$ is supported on $S ∖ A$ and has the local finite normal form

t^{\circ} = ∣ γ ∣ \leq r \sum E_{γ} b_{γ}^{\circ}, b_{γ}^{\circ} \in D^{'} (X ∖ Z) .

The equality is understood in product neighborhoods contained in $U ∖ A$ that meet $S$ ; away from $S$ , the distribution is zero.

A supported realization of normal order at most $r$ means a distribution supported in $S$ that annihilates tests whose normal jets through order $r$ vanish. This is the support-explicit convention of XV-B.

Displayed formulas in this passage

XV-C@1#eq:puncturedform · line 969
$t^{\circ} = ∣ γ ∣ \leq r \sum E_{γ} b_{γ}^{\circ}, b_{γ}^{\circ} \in D^{'} (X ∖ Z) .$
unlabeled · line 960
$U = X \times V_{q}, S = X \times {0} .$
unlabeled · line 964
$Z = {x \in X : (x, 0) \in A} .$

Local geometric hypotheses

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