Expand all Collapse all  Results 26  49 of 49 
26. CMB 2005 (vol 48 pp. 340)
Short Geodesics of Unitaries in the $L^2$ Metric Let $\M$ be a type II$_1$ von Neumann algebra, $\tau$ a trace in $\M$,
and $\l2$ the GNS Hilbert space of $\tau$. We regard the unitary group
$U_\M$ as a subset of $\l2$ and characterize the shortest smooth
curves joining two fixed unitaries in the $L^2$ metric. As a
consequence of this we obtain that $U_\M$, though a complete (metric)
topological group, is not an embedded riemannian submanifold of $\l2$
Keywords:unitary group, short geodesics, infinite dimensional riemannian manifolds. Categories:46L51, 58B10, 58B25 
27. CMB 2005 (vol 48 pp. 283)
Enlarged Inclusion of Subdifferentials This paper studies the integration of inclusion of subdifferentials. Under
various verifiable conditions, we obtain that if two proper lower
semicontinuous functions $f$ and $g$ have the subdifferential of $f$
included in the $\gamma$enlargement of the subdifferential of $g$, then
the difference of those functions is $ \gamma$Lipschitz over their
effective domain.
Keywords:subdifferential,, directionally regular function,, approximate convex function,, subdifferentially and directionally stable function Categories:49J52, 46N10, 58C20 
28. CMB 2004 (vol 47 pp. 624)
A Compactness Theorem for YangMills Connections In this paper, we consider YangMills connections
on a vector bundle $E$ over a compact Riemannian manifold $M$ of
dimension $m> 4$, and we show that any set of YangMills
connections with the uniformly bounded $L^{\frac{m}{2}}$norm of
curvature is compact in $C^{\infty}$ topology.
Keywords:YangMills connection, vector bundle, gauge transformation Categories:58E20, 53C21 
29. CMB 2004 (vol 47 pp. 607)
A Residue Formula for $\SU(2)$Valued Moment Maps Jeffrey and Kirwan gave expressions
for intersection pairings on the reduced space
$M_0=\mu^{1}(0)/G$ of a Hamiltonian $G$space $M$
in terms of multiple residues.
In this paper we prove a residue formula for
symplectic volumes of reduced spaces of a quasiHamiltonian
$\SU(2)$space. The definition of quasiHamiltonian
$G$spaces was recently introduced in .
Category:58F05 
30. CMB 2004 (vol 47 pp. 515)
Remarques sur l'enlacement en thÃ©orie des points critiques pour des fonctionnelles continues Dans cet article, \`a partir de la notion d'enlacement introduite
dans ~\cite{F} entre des paires d'ensembles $(B,A)$ et $(Q,P)$,
nous \'etablissons l'existence d'un point critique d'une
fonctionnelle continue sur un espace m\'etrique lorsqu'une de ces
paires enlace l'autre. Des renseignements sur la localisation du
point critique sont aussi obtenus. Ces r\'esultats conduisent \`a
une g\'en\'eralisation du th\'eor\`eme des trois points critiques.
Finalement, des applications \`a des probl\`emes aux limites pour
une \'equation quasilin\'eaire elliptique sont pr\'esent\'ees.
Categories:58E05, 35J20 
31. CMB 2003 (vol 46 pp. 481)
On the Composition of Differentiable Functions We prove that a Banach space $X$ has the Schur property if and only if every
$X$valued weakly differentiable function is Fr\'echet differentiable. We
give a general result on the Fr\'echet differentiability of $f\circ T$, where
$f$ is a Lipschitz function and $T$ is a compact linear operator. Finally
we study, using in particular a smooth variational principle, the
differentiability of the semi norm $\Vert \ \Vert_{\lip}$ on various spaces
of Lipschitz functions.
Categories:58C20, 46B20 
32. CMB 2002 (vol 45 pp. 378)
The Local MÃ¶bius Equation and Decomposition Theorems in Riemannian Geometry A partial differential equation, the local M\"obius equation, is
introduced in Riemannian geometry which completely characterizes the
local twisted product structure of a Riemannian manifold. Also the
characterizations of warped product and product structures of
Riemannian manifolds are made by the local M\"obius equation and an
additional partial differential equation.
Keywords:submersion, MÃ¶bius equation, twisted product, warped product, product Riemannian manifolds Categories:53C12, 58J99 
33. CMB 2002 (vol 45 pp. 97)
Invariant Measures and Natural Extensions We study ergodic properties of a family of interval maps that are
given as the fractional parts of certain real M\"obius
transformations. Included are the maps that are exactly
$n$to$1$, the classical Gauss map and the Renyi or backward
continued fraction map. A new approach is presented for deriving
explicit realizations of natural automorphic extensions and their
invariant measures.
Keywords:Continued fractions, interval maps, invariant measures Categories:11J70, 58F11, 58F03 
34. CMB 2002 (vol 45 pp. 3)
RealAnalytic Negligibility of Points and Subspaces in Banach Spaces, with Applications We prove that every infinitedimensional Banach space $X$ having a
(not necessarily equivalent) realanalytic norm is realanalytic
diffeomorphic to $X \setminus \{0\}$. More generally, if $X$ is an
infinitedimensional Banach space and $F$ is a closed subspace of $X$
such that there is a realanalytic seminorm on $X$ whose set of zeros
is $F$, and $X/F$ is infinitedimensional, then $X$ and $X \setminus
F$ are realanalytic diffeomorphic. As an application we show the
existence of realanalytic free actions of the circle and the
$n$torus on certain Banach spaces.
Categories:46B20, 58B99 
35. CMB 2001 (vol 44 pp. 376)
A Note on $p$Harmonic $1$Forms on Complete Manifolds In this paper we prove that there is no nontrivial $L^{q}$integrably
$p$harmonic $1$form on a complete manifold with nonnegatively Ricci
curvature $(0

36. CMB 2001 (vol 44 pp. 323)
Une classe d'hamiltoniens polynomiaux isochrones Soit $H_0 = \frac{x^2+y^2}{2}$ un hamiltonien isochrone du plan
$\Rset^2$. On met en \'evidence une classe d'hamiltoniens isochrones
qui sont des perturbations polynomiales de $H_0$. On obtient alors
une condition n\'ecessaire d'isochronisme, et un crit\`ere de choix
pour les hamiltoniens isochrones. On voit ce r\'esultat comme \'etant
une g\'en\'eralisation du caract\`ere isochrone des perturbations
hamiltoniennes homog\`enes consid\'er\'ees dans [L], [P], [S].
Let $H_0 = \frac{x^2+y^2}{2}$ be an isochronous Hamiltonian of the
plane $\Rset^2$. We obtain a necessary condition for a system to be
isochronous. We can think of this result as a generalization of the
isochronous behaviour of the homogeneous polynomial perturbation of
the Hamiltonian $H_0$ considered in [L], [P], [S].
Keywords:Hamiltonian system, normal forms, resonance, linearization Categories:34C20, 58F05, 58F22, 58F30 
37. CMB 2001 (vol 44 pp. 129)
LinÃ©arisation symplectique en dimension 2 In this paper the germ of neighborhood of a compact leaf in a
Lagrangian foliation is symplectically classified when the compact
leaf is $\bT^2$, the affine structure induced by the Lagrangian
foliation on the leaf is complete, and the holonomy of $\bT^2$ in
the foliation linearizes. The germ of neighborhood is classified by a
function, depending on one transverse coordinate, this function is
related to the affine structure of the nearly compact leaves.
Keywords:symplectic manifold, Lagrangian foliation, affine connection Categories:53C12, 58F05 
38. CMB 2001 (vol 44 pp. 210)
Growth Estimates on Positive Solutions of the Equation $\Delta u+K u^{\frac{n+2}{n2}}=0$ in $\R^n$ We construct unbounded positive $C^2$solutions of the equation
$\Delta u + K u^{(n + 2)/(n  2)} = 0$ in $\R^n$ (equipped
with Euclidean metric $g_o$) such that $K$ is bounded between two
positive numbers in $\R^n$, the conformal metric $g=u^{4/(n2)}g_o$
is complete, and the volume growth of $g$ can be arbitrarily fast
or reasonably slow according to the constructions. By imposing natural
conditions on $u$, we obtain growth estimate on the $L^{2n/(n2)}$norm
of the solution and show that it has slow decay.
Keywords:positive solution, conformal scalar curvature equation, growth estimate Categories:35J60, 58G03 
39. CMB 2001 (vol 44 pp. 160)
The Trace Formula and Its Applications: An Introduction to the Work of James Arthur James Arthur was awarded the Canada Gold Medal of the National
Science and Engineering Research Council in 1999. This
introduction to his work is an attempt to explain his methods and
his goals to the mathematical community at large.
Categories:11F70, 11F72, 58G25 
40. CMB 2001 (vol 44 pp. 140)
On Quantizing Nilpotent and Solvable Basic Algebras We prove an algebraic ``nogo theorem'' to the effect that a
nontrivial \pa\ cannot be realized as an associative algebra with the
commu\ta\tor bracket. Using it, we show that there is an
obstruction to quantizing the \pa\ of polynomials generated by a
nilpotent \ba\ on a \sm. This result generalizes \gr 's famous
theorem on the impossibility of quantizing the Poisson algebra of
polynomials on $\r^{2n}$. Finally, we explicitly construct a
polynomial quantization of a \sm\ with a solvable \ba, thereby showing
that the obstruction in the nilpotent case does not extend to the
solvable case.
Categories:81S99, 58F06 
41. CMB 2001 (vol 44 pp. 105)
Convolution Equation in $\mathcal{S}^{\prime\ast}$Propagation of Singularities The singular spectrum of $u$ in a convolution equation $\mu * u = f$,
where $\mu$ and $f$ are tempered ultradistributions of Beurling or
Roumieau type is estimated by
$$
SS u \subset (\mathbf{R}^n \times \Char \mu) \cup SS f.
$$
The same is done for $SS_{*}u$.
Categories:32A40, 46F15, 58G07 
42. CMB 2000 (vol 43 pp. 427)
Helices, Hasimoto Surfaces and BÃ¤cklund Transformations Travelling wave solutions to the vortex filament flow generated by
elastica produce surfaces in $\R^3$ that carry mutually orthogonal
foliations by geodesics and by helices. These surfaces are classified
in the special cases where the helices are all congruent or are all
generated by a single screw motion. The first case yields a new
characterization for the B\"acklund transformation for constant
torsion curves in $\R^3$, previously derived from the wellknown
transformation for pseudospherical surfaces. A similar investigation
for surfaces in $H^3$ or $S^3$ leads to a new transformation for
constant torsion curves in those spaces that is also derived from
pseudospherical surfaces.
Keywords:surfaces, filament flow, BÃ¤cklund transformations Categories:53A05, 58F37, 52C42, 58A15 
43. CMB 2000 (vol 43 pp. 183)
A Gauge Theoretic Proof of the AbelJacobi Theorem We present a new, simple proof of the classical AbelJacobi theorem
using some elementary gauge theoretic arguments.
Keywords:AbelJacobi theorem, abelian gauge theory Categories:58D27, 30F99 
44. CMB 2000 (vol 43 pp. 25)
Subdifferential Regularity of Directionally Lipschitzian Functions Formulas for the Clarke subdifferential are always expressed in the
form of inclusion. The equality form in these formulas generally
requires the functions to be directionally regular. This paper
studies the directional regularity of the general class of
extendedrealvalued functions that are directionally Lipschitzian.
Connections with the concept of subdifferential regularity are also
established.
Keywords:subdifferential regularity, directional regularity, directionally Lipschitzian functions Categories:49J52, 58C20, 49J50, 90C26 
45. CMB 2000 (vol 43 pp. 51)
Eigenfunction Decay For the Neumann Laplacian on HornLike Domains The growth properties at infinity for eigenfunctions corresponding to
embedded eigenvalues of the Neumann Laplacian on hornlike domains
are studied. For domains that pinch at polynomial rate, it is shown
that the eigenfunctions vanish at infinity faster than the reciprocal
of any polynomial. For a class of domains that pinch at an exponential
rate, weaker, $L^2$ bounds are proven. A corollary is that eigenvalues
can accumulate only at zero or infinity.
Keywords:Neumann Laplacian, hornlike domain, spectrum Categories:35P25, 58G25 
46. CMB 1999 (vol 42 pp. 478)
A Remark On the MoserAubin Inequality For Axially Symmetric Functions On the Sphere Let $\scr S_r$ be the collection of all axially symmetric functions
$f$ in the Sobolev space $H^1(\Sph^2)$ such that $\int_{\Sph^2}
x_ie^{2f(\mathbf{x})} \, d\omega(\mathbf{x})$ vanishes for $i=1,2,3$.
We prove that
$$
\inf_{f\in \scr S_r} \frac12 \int_{\Sph^2} \nabla f^2 \, d\omega
+ 2\int_{\Sph^2} f \, d\omega \log \int_{\Sph^2} e^{2f} \, d\omega > \oo,
$$
and that this infimum is attained. This complements recent work of
Feldman, Froese, Ghoussoub and Gui on a conjecture of Chang and Yang
concerning the MoserAubin inequality.
Keywords:Moser inequality, borderline Sobolev inequalities, axially symmetric functions Categories:26D15, 58G30 
47. CMB 1997 (vol 40 pp. 271)
Nonreal periodic points of entire functions It is shown that if $f$ is an entire transcendental function, $l$ a straight
line in the complex plane, and $n\geq 2$, then $f$ has infinitely many
repelling periodic points of period $n$ that do not lie on $l$.
Categories:30D05, 58F23 
48. CMB 1997 (vol 40 pp. 285)
The space of harmonic maps from the $2$sphere to the complex projective plane In this paper we study the topology of the space of harmonic maps
from $S^2$ to $\CP 2$. We prove that the subspaces consisting of maps of a
fixed degree and energy are path connected. By a result of Guest and Ohnita
it follows that the same is true for the space of harmonic maps to $\CP n$
for $n\geq 2$. We show that the components of maps to $\CP 2$ are complex
manifolds.
Categories:58E20, 58D27 
49. CMB 1997 (vol 40 pp. 204)
The $\eta$invariants of cusped hyperbolic $3$manifolds In this paper, we define the $\eta$invariant for a cusped hyperbolic
$3$manifold and discuss some of its applications. Such an
invariant detects the chirality of a hyperbolic knot or link and
can be used to distinguish many links with homeomorphic complements.
Categories:57M50, 53C30, 58G25 