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Project Euclid (Hosted at Cornell University Library) (192.977 recursos)
Communications in Analysis and Geometry
Communications in Analysis and Geometry
Charbonneau, Benoit
The main result is a computation of the Nahm transform of a $\SUt$-instanton
over $\R\times T^3$, called spatially-periodic instanton. It is a singular
monopole over $T^3$, a solution to the Bogomolny equation, whose rank is
computed and behavior at the singular points is described.
Ammann, Bernd; Humbert, Emmanuel; Morel, Bertrand
1Let $M$ be a compact manifold equipped with a Riemannian metric $g$ and a
spin structure $\si$.
We let $\lamin (M,[g],\si)= \inf_{\tilde{g} \in [g] } \lambda_1^+(\tilde{g})
Vol(M,\tilde{g})^{1/n} $ where $\lambda_1^+(\tilde{g})$ is the
smallest positive eigenvalue of the
Dirac operator $D$ in the metric $\tilde{g}$.
A previous result stated that $\lamin(M,[g],\si) \leq \lamin(\mS^n) =\frac{n}{2} \om_n^{{1/n}}$
where $\om_n$ stands for the volume of the standard
$n$-sphere.
%The inequality is strict when $n \geq 7$ and $(M,g)$ is not conformally flat.
In this paper, we study this problem for conformally flat
manifolds of dimension $n \geq 2$ such that $D$ is invertible. E.g., we show that strict inequality holds in dimension
$n\equiv 0,1,2\mod 4$ if...
Thomas, R. P.
We find stability conditions [6,3] on
some derived categories of differential graded modules over a graded
algebra studied in [12,10]. This category arises in both derived
Fukaya categories and derived categories of coherent sheaves. This
gives the first examples of stability conditions on the A-model side of
mirror symmetry, where
the triangulated category is not naturally the derived category of an abelian
category. The existence of stability conditions, however, gives many such
abelian categories, as predicted by mirror symmetry.
¶ In our examples in 2 dimensions, we completely
describe a connected component of the space of stability conditions. It is
the universal cover of the configuration space $C_{k+1}^0$ of $k+1$
points in...
Lee, Junho
We explicitly compute family GW invariants of elliptic surfaces
for primitive classes. That involves establishing a TRR formula
and a symplectic sum formula for elliptic surfaces and then
determining the GW invariants using an argument from [9].
In particular, as in [2], these calculations also
confirm the well-known Yau--Zaslow Conjecture [22] for
primitive classes in $K3$ surfaces.
Hang, Fengbo; Wang, Xiaodong
Hu, Shengda
We provide a construction of examples of semistable degeneration via toric geometry. The applications include a higher dimensional generalization of classical degeneration of $K3$ surface into 4 rational components, an algebraic geometric version of decomposing $K3$ as the fiber sum of two $E(1)$'s as well as it's higher dimensional generalizations and many other new examples.
Harvey, Reese; Lawson, Blaine
We introduce a new homological machine for the study of secondary
geometric invariants. The objects, called spark complexes, occur in many
areas of mathematics. The theory is applied here to establish the
equivalence of a large family of spark complexes which appear naturally in
geometry, topology and physics. These complexes are quite different. Some
of them are purely analytic, some are simplicial, some are of
?ech-type, and many are mixtures. However, the associated theories of
secondary invariants are all shown to be canonically isomorphic.
Numerous applications and examples are explored.
Ruan, Wei--Dong
In this paper, we prove that the Kähler-Einstein metrics for a toroidal canonical degeneration family of Kähler manifolds with ample canonical bundles Gromov--Hausdorff converge to the complete Kähler-Einstein metric on the smooth part of the central fiber when the base locus of the degeneration family is empty. We also prove the incompleteness of the Weil--Peterson metric in this case.
Weitsman, Allen
We consider minimal graphs $\ u=u(x,y)>0$ over unbounded domains D
with $\ u=0$ on $\partial D$. We shall study the rates at which
$u$ can grow when $D$ is contained in a half plane.
Wang, Shaobo; Yau, Stephen S.-T.
An arrangement of hyperplanes is a finite collection of {\bf C}-linear subspaces of codimension one in a complex vector space ${\bf C}^l$. For such an arrangement ${\cal A}$, there is a natural projective arrangement ${\cal A}^*$ of hyperplanes in ${\bf CP}^{l-1}$ associated to it. Let $M({\cal A})={\bf C}^l- \bigcup_{H \in {\cal A}} H$ and $M({\cal A}^*)= {\bf CP}^{l-1}- \bigcup_{H^* \in {\cal A}^*}H^*$.
One of central topics in the theory of arrangements is to find connections between the topology or differentiable structure of $M({\cal A})$ (or $M({\cal A}^*)$) and the combinatorial geometry of ${\cal A}$. A partial solution to this problem was...
Topping, Peter
We estimate the diameter of a closed manifold evolving under Ricci flow
in terms of a scalar curvature integral. The proof uses a
new maximal function and extends some of Perelman's recent ideas.
Lotay, Jason
Wang, Mu-Tao
\Let $M=\Sigma_1\times \Sigma_2$ be the product of two compact
Riemannian manifolds of dimension $n\geq 2 $ and two,
respectively. Let $\Sigma$ be the graph of a smooth map
$f:\Sigma_1\rightarrow \Sigma_2$; $\Sigma$ is an $n$-dimensional
submanifold of $M$. Let ${\frak G}$
be the Grassmannian bundle over $M$ whose fiber at each point is the set of
all $n$-dimensional subspaces of the tangent space of $M$.
The Gauss map $\gamma:\Sigma\rightarrow \frak{G} $ assigns to each
point $x\in \Sigma$ the tangent space of $\Sigma$ at $x$. This
article considers the mean curvature flow of $\Sigma$ in $M$. When
$\Sigma_1$ and $\Sigma_2$ are of
the same non-negative curvature, we show a sub-bundle $\frak{S}$
of the Grassmannian...
Andersson, Lars
Benedetti and Guadagnini [5]
have conjectured that the constant mean curvature
foliation $M_\tau$
in a $2+1$ dimensional flat spacetime $V$ with compact hyperbolic Cauchy surfaces satisfies
$\lim_{\tau \to -\infty} \ell_{M_\tau} = s_{\Tree}$, where $\ell_{M_\tau}$
and $s_{\Tree}$ denote the marked length spectrum of $M_\tau$ and the marked
measure spectrum of the $\Re$-tree $\Tree$, dual to the measured foliation
corresponding to the translational part of the holonomy of $V$,
respectively. We prove that this is the case for $n+1$ dimensional, $n \geq
2$, simplicial flat
spacetimes with compact hyperbolic Cauchy surface. A simplicial spacetime is
obtained from the Lorentz cone over a hyperbolic manifold by deformations
corresponding to a simple measured foliation.
Qiu, Ruifeng; Wang, Shicheng
We construct a hyperbolic 3-manifold $M$ (with $\partial
M$ totally geodesic) which contains no essential closed surfaces,
but for any even integer $g> 0$, there are infinitely many
separating slopes $r$ on $\partial M$ so that $M[r]$, the
3-manifold obtained by attaching 2-handle to $M$ along $r$,
contains an essential separating closed surface of genus $g$ and
is still hyperbolic. The result contrasts sharply with those
known finiteness results for the cases $g=0,1$. Our 3-manifold $M$
is the complement of a simple small knot in a handlebody.
Hang, Fengbo
We identify all the weak sequential limits of smooth maps in $W^{1,2}\left(
M,N\right) $. In particular, this implies a necessary and sufficient
topological condition for smooth maps to be weakly sequentially dense in
$W^{1,2}\left( M,N\right) $.
Bachman, David; Schleimer, Saul
This paper studies Heegaard splittings of surface bundles via the
curve complex of the fibre. The translation distance of the
monodromy is the smallest distance it moves any vertex of the curve
complex. We prove that the translation distance is bounded above in
terms of the genus of any strongly irreducible Heegaard splitting. As
a consequence, if a splitting surface has small genus compared to the
translation distance of the monodromy, then the splitting is standard.
Guan, Pengfei; Lin, Chang-Shou; Wang, Guofang
In this paper, we prove a cohomology
vanishing theorem on locally conformally flat manifold
under certain positivity assumption
on the Schouten tensor. And we show that this type of positivity
of curvature is preserved under $0$-surgeries for general
Riemannian manifolds, and construct a large class of such
manifolds.
Bartnik, Robert
A Hilbert manifold structure is described for the phase space $\cF$
of asymptotically flat initial data for the Einstein equations. The
space of solutions of the constraint equations forms a Hilbert
submanifold $\cC \subset \cF$. The ADM energy-momentum defines a function which is
smooth on this submanifold, but which is not defined in general on
all of $\cF$. The ADM Hamiltonian defines a smooth function on $\cF$
which generates the Einstein evolution equations only if the
lapse-shift satisfies rapid decay conditions. However a regularised
Hamiltonian can be defined on $\cF$ which agrees with the
Regge-Teitelboim Hamiltonian on $\cC$ and generates the evolution
for any lapse-shift appropriately asymptotic to a (time)...
Jin, Ning; Yau, Stephen S. T.
In [14], Ngai and Wang introduced the concept of finite type IFS to
study the Hausdorff dimension of self-similar sets without open set
condition. In this paper, by applying the M-matrix theory([15]),
we generalize the notion of finite type IFS to the general finite type
IFS.
A family of IFS with $3$ parameters, but without open set condition
is presented. The Hausdorff dimension of the associated attractors
can be calculated by both the $M$-matrix method and the general
finite type IFS method. But these IFS are not finite type except
for those parameters lying in a set of measure zero.