Tài liệu Đề tài " The causal structure of microlocalized rough Einstein metrics " pptx
Tài liệu Đề tài " The causal structure of microlocalized rough Einstein metrics " pptx
... that
Q[H](T,L)=
1
2
(LH)
2
+
1
2
|∇/H|
2
=
1
2
|D
∗
H|
2
,
Q[H](T,T)=
1
2
(TH)
2
+
1
2
|∇H|
2
=
1
2
|∂H|
2
.
Annals of Mathematics, 161 (2005), 1195–1243
The causal structure of
microlocalized rough Einstein metrics
By Sergiu Klainerman and Igor Rodnianski
Abstract
This is the second in a series of three ... in the derivation of the decay estimates needed in the...
Tài liệu Đề tài " Hausdorff dimension of the set of nonergodic directions " ppt
... q)=1}
area(Σ)
.
R
2R
2/Q
α
Figure 2. The parallelogram Σ(α, R, Q).
The proof of Theorem 2 relies on the following fact:
Theorem 3. Let Spec(α) be the sequence of heights formed by the
convergents of α. There exist constants ... Roth’s theorem every algebraic integer satisfies the hypothesis of Theorem 1.
Some generalizations of Theorem 1 are mentioned in Section 2. For...
Tài liệu Đề tài " On the volume of the intersection of two Wiener sausages " ppt
... yields the claim in (2.80). This completes the proof of
Lemma 6.
This completes the proof of Proposition 4 and hence of Theorem 1.
3. Proof of Theorem 2
In this section we indicate how the arguments ... second
term on the right-hand side of the analogue of (2.93).
4. Proof of Theorem 3
In Sections 4–6 we prove Theorems 3–5. The proof follows the same line
of re...
Tài liệu Đề tài " Geometry of the uniform spanning forest: Transitions in dimensions 4, 8, 12, . . . " pptx
... and let F
n
be the union of F
n−1
with the loop-erasure of X
n
. Then F :=
∞
n=1
F
n
has the distribution of the
(wired) USF on G. The edges in F inherit the orientation from the loop-erased
walks ... occurrence
of S, then we should also contract the edges in K
1
and delete the edges in K
2
.
Therefore, conditionally on Υ
R
and the occurrence of S, the path γ...
Tài liệu Đề tài " The space of embedded minimal surfaces of fixed genus in a 3-manifold III; Planar domains " doc
... graph. (The existence of the curves σ
1
, γ
1
, γ
2
will be established
in the next section.) First we need two lemmas. The first of these is the
following:
Lemma II.1.38. Given C
1
,ε
0
> 0, there ... σ
2
.
The next lemma bounds the area of a minimal surface with two sides and
an interior boundary in a small ball in terms of the length of the sides, provided
that...
Tài liệu Đề tài " Statistical properties of unimodal maps: the quadratic family " pptx
... ∈
Ξ
i
(C
d
i
) ∩F
κ
then Ξ
i
(C
d
i
)=J
i+1
[g].
We will concentrate on the analysis of the regularity of Ξ
i
for the spe-
cial class of simple maps f: one of the good properties of the class of simple
maps ... describe the general
strategy behind the proofs of Theorems A and B.
(1) We consider a certain set of nonregular parameters of full measure
and describe...
Tài liệu Đề tài " On the holomorphicity of genus two Lefschetz fibrations " pptx
... from the set of irreducible components of C
∞
to the set of
irreducible components of C
n
. The claim on semi-continuity of m follows once
we show that the sum of the multiplicities of the components ... between the irreducible components of |C
n
| and of |C
∞
|
respecting the genera.
Proof. By the definition of the cycle topology, for n 0 each compone...
Tài liệu Đề tài " Rough solutions of the Einstein-vacuum equations " docx
... in the proof of (93). The remaining term on the left-hand side of
(93) is easier to treat.
7. Proof of the L
2
− L
∞
decay estimate; Theorem 2.1
In this section we rely on the Boundedness Theorem ... u.
With the help of these constructions the proof of the L
2
− L
∞
decay
estimate stated in Theorem 2.1 can be reduced to the following:
Theorem 3.4 (Boundedness Theor...
Tài liệu Đề tài " Asymptotic faithfulness of the quantum SU(n) representations of the mapping class groups " pdf
... multiple of the identity. We
will suppress the superscript on the quantum representations and simply write
ρ
k
= ρ
n,d
k
throughout the rest of the paper.
Our key idea in the proof of Theorem 1 is the ... (see the proof of Theorem 7). Theorem 1 now follows directly
from knowing which elements of the mapping class group act trivially on the
moduli space M.
The a...
Tài liệu Đề tài " The resolution of the Nirenberg-Treves conjecture " docx
... C
u
2
(2.17)
and the estimate (2.11), which completes the proof of Theorem 1.1.
It remains to prove Proposition 2.5, which will be done at the end of
Section 7. The proof involves the construction of a multiplier ... gradient of the imagi-
nary part is nonvanishing, so that the zeroes form a smooth submanifold. The
estimate uses a new type of weight, which measur...
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