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

Exact initial-surface support

A fully specified flat realization and the solid-ball error › Exact initial-surface support · lines 698–722

IX-E-3@1#eq:SF, IX-E-3@1#eq:NF

For $f \in C_{c}^{\infty} (M_{+}^{\circ})$ , define compact sets

S_{F} N_{F} = {z : \exists (t, x) \in F, ∣ z - x ∣ = t}, = {(v, z) : \exists (t, x) \in F, 0 \leq v \leq t, ∣ z - x ∣ = t - v} .

The first is a union of initial null spheres. The second is the union of their truncated backward null cones.

Displayed formulas in this passage

IX-E-3@1#eq:SF · line 701
$S_{F} N_{F} = {z : \exists (t, x) \in F, ∣ z - x ∣ = t}, = {(v, z) : \exists (t, x) \in F, 0 \leq v \leq t, ∣ z - x ∣ = t - v} .$
IX-E-3@1#eq:NF · line 701
$S_{F} N_{F} = {z : \exists (t, x) \in F, ∣ z - x ∣ = t}, = {(v, z) : \exists (t, x) \in F, 0 \leq v \leq t, ∣ z - x ∣ = t - v} .$