Manuscript XI-G@1 · XI-G.tex · definition · f029bbcd

Definition: Free-shell class

The question, written so it cannot collapse · lines 576–589

XI-G@1#def:class

Let $u$ be the frozen kernel of $C_{3} (f, g)$ . A compactly supported distribution $v$ on $M^{3}$ , with two symmetric-tensor slots and one scalar slot and symmetric in the tensor slots, belongs to $[u]_{sol}$ if

⟨ v - u, γ_{1} \otimes γ_{2} \otimes ϕ ⟩ = 0 for all smooth γ_{1}, γ_{2} with □ γ_{a} = 0 and all smooth ϕ with P_{m} ϕ = 0.

Real and complex solutions are equivalent here by bilinearity. We say that $[u]_{sol}$ {meets $F_{mc, pol}$ } if some $v \in [u]_{sol}$ satisfies (eq:mc) with $n = 3$ .

Displayed formulas in this passage

unlabeled · line 581
$⟨ v - u, γ_{1} \otimes γ_{2} \otimes ϕ ⟩ = 0 for all smooth γ_{1}, γ_{2} with □ γ_{a} = 0 and all smooth ϕ with P_{m} ϕ = 0.$

Nearby in this section

lemma: Lemma: Reduction to one kernel
section: The question, written so it cannot collapse