... infinity
(the existence of a supercompact cardinal) that the class of uncountable linear
orders has a five element basis. In fact such a basis follows from the Proper
Forcing Axiom, a strong form of the ... basis for the class of uncountable separable linear
orders.
PFA is a strengthening of the Baire Category Theorem and is independent
of the usual...
... B
i
and a probability measure
µ supported on K
η
satisfying the condition that for an arbitrary ball A of
sufficiently small radius r (A)
µ (A)
V
f
(A)
η
,(13)
where the implied constant in the ... Falconer, Fractal Geometry: Mathematical Foundations and Applications, John Wi-
ley & Sons, New York (1990).
[4]
P. X. Gallagher, Metric simultaneous diophantine approximation. I...
... in an “unacceptably”
smooth Denjoy map and vector field.
University of California, Santa Cruz, CA 95064, USA
E-mail address: ginzburg@math.ucsc.edu
University of California, Santa Cruz, CA, USA
Current ... condition:Iftwo points (a, x), the
“entrance”, and (b, y), the “exit”, are on the same characteristic, then
x = y.Inother words, for a characteristic that meets both the bottom
a...
... of the
M
j
’s as j → ∞. Then one can show that M
∗
is translationally invariant.
The translational invariance means that M
∗
is the Cartesian product
with R of a flow M of m-dimensional surfaces ... for the heat equation, and we derive the nonparamet-
ric equations for mean curvature flow. First we recall the definitions of the
Annals of Mathematics, 161 (2005), 1487–1519...
... that
G(u) ≤ ε
1
, and similarly (4.4) must also hold for u
h
.
Annals of Mathematics
Sharp local well-
posedness results
for the nonlinear
wave equation
By Hart F. Smith and Daniel Tataru ... is essentially a variation on the theme of characteristic
energy estimates for the variable coefficient wave equation. The assumption
on G(u) implies that each Σ
θ,r
is the graph o...
... (Operator Theory: Advances and Applications 108), 129–148, Birkh¨auser,
Basel, 1999.
Annals of Mathematics, 166 (2007), 549–577
On Mott’s formula for the ac-conductivity
in the Anderson model
By Abel ... →φ, A
ω
φ are measurable for all φ ∈H
c
,
A is covariant if
U(x )A
ω
U(x)
∗
= A
τ
x
(ω)
for all x ∈ Z
d
,(3.9)
and A is locally bounded if A
ω
χ
x
< ∞ and
χ
x
A...
... 6.2 a result that will play a crucial
role for the Paley-Wiener theorem. It shows that Arthur-Campoli functionals
on the smaller symmetric space X
F,v
induce Arthur-Campoli functionals on
the ... exists a Hom(
◦
C,V)-
valued Laurent functional L
∈ L⊗V ⊂M (a
∗
q
C
, Σ)
∗
laur
⊗Hom(
◦
C,V) such
that f
ψ
= L
ψ for all ψ.
We first formulate a result in linear algebra, and...
... less than 1).
Then there are a dense f-invariant subset
˜
Σ of Σ and an ε-perturbation
ˆ
A of A such that for any y ∈
˜
Σ the linear map M
ˆ
A
(y) is either a dilation or a
contraction (according ... if
necessary the rectangles of the Markov partition, we can assume that, for any
x and y in the same rectangle,
A( x) − A( y) <ε and A
−1
(x) − A
−1
(y) <ε....