diff dad58ff..763cb89 spacetime_penrose_area_charge_v2.txt
diff --git a/spacetime_penrose_area_charge_v2.txt b/spacetime_penrose_area_charge_v2.txt
index 635d860..7ffad31 100644
--- a/spacetime_penrose_area_charge_v2.txt
+++ b/spacetime_penrose_area_charge_v2.txt
@@ -141,13 +141,13 @@ contributions end and the classical machinery begins.
energy $E_h$, and $\partial N$ is a compact outermost smooth minimal
surface of total area $A$, then $E_h\ge\sqrt{A/16\pi}$, with equality
in the nondegenerate case exactly for the Schwarzschild horizon.
-./bray-2001.pdf ./huisken-ilmanen-2001.pdf
+./pdf/bray-2001.pdf ./huisken-ilmanen-2001.pdf
(T2) Positive mass theorem (Schoen--Yau 1979, Witten 1981). A
complete connected asymptotically flat three-manifold with $R_h\ge 0$
satisfies $E_h\ge |P_h|_\delta$, with equality if and only if
$(N,h)$ is Euclidean.
-./schoen-yau-1979.pdf ./witten-1981.pdf
+./pdf/schoen-yau-1979.pdf ./witten-1981.pdf
(T3) Static vacuum uniqueness (Bunting--Masood-ul-Alam 1987).
A complete three-dimensional static vacuum data set $(N,h,N)$ with
@@ -160,7 +160,7 @@ contributions end and the classical machinery begins.
same setup with total charge $Q=(Q_E^2+Q_B^2)^{1/2}$ and $P=0$ gives
$E_h\ge Q$ and $r\le m+\sqrt{m^2-Q^2}$, with $r=(A/4\pi)^{1/2}$ and
$m=E_h$.
-./disconzi-khuri-2012.pdf
+./pdf/disconzi-khuri-2012.pdf
Everything else (strictification, rest-frame reduction, the coupled
elliptic construction, the causal stationary field, the charge and
@@ -1353,7 +1353,7 @@ has uniformly bounded geometry (since $\bar g$ does and $f$ is smooth),
and has finite three-volume $V_Q=\operatorname{Vol}_{\Gamma_f}(\pi^{-1}Q)$.
By the Nash embedding theorem (Nash 1956, Theorem 2), a fixed compact enlargement
of $\Gamma_f$ embeds isometrically in some $\mathbb{R}^N$.
-./nash-1956.pdf
+./pdf/nash-1956.pdf
The standard
submanifold Sobolev embedding for compactly supported functions then
gives, in dimension $3$,
@@ -1599,7 +1599,7 @@ $f$-equation is Dirichlet-elliptic with invertible principal part, and
the $Z$-equation on the mixed Neumann--Dirichlet problem is invertible
with strictly positive Green function. The Leray--Schauder degree of
the linear solve operator is therefore one.
-./leray-schauder-1934.pdf
+./pdf/leray-schauder-1934.pdf
Continuation in each
parameter is legitimate because the [prop:n3:apriori] proposition
supplies uniform bounds on the range, and