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Geography of symplectic 4- and 6-manifolds
Symplectic geography symplectic sums symplectic structures
2011/9/15
Abstract: The geography of minimal symplectic 4-manifolds with arbitrary fundamental group and symplectic 6-manifolds with abelian fundamental group of small rank, and with arbitrary fundamental group...
Birational superrigidity and slope stability of Fano manifolds
Birational superrigidity Fano manifolds Algebraic Geometry
2011/9/15
Abstract: We show a relation between the birational superrigidity of Fano manifold and its slope stability in the sense of Ross-Thomas.
Caccioppoli's inequalities on constant mean curvature hypersurfaces in Riemannian manifolds
Caccioppoli’s inequality Simons’ equation constant mean curvature hypersurfaces stable finite index
2011/9/14
Abstract: We prove some Caccioppoli's inequalities for the traceless part of the second fundamental form of a complete, non compact, finite index, constant mean curvature hypersurface of a Riemannian ...
Algebra properties for Sobolev spaces- Applications to semilinear PDE's on manifolds
Sobolev spaces Riemannian manifold algebra rule paraproducts heat semigroup
2011/9/15
Abstract: In this work, we aim to prove algebra properties for generalized Sobolev spaces $W^{s,p} \cap L^\infty$ on a Riemannian manifold, where $W^{s,p}$ is of Bessel-type $W^{s,p}:=(1+L)^{-s/m}(L^p...
The twisted Alexander polynomial for finite abelian covers over three manifolds with boundary
Reidemeister torsion:Twisted Alexander polynomial:branched cover:links:Homology orientation
2011/9/13
Abstract: We consider a sign--determined Reidemeister torsion with multivariables for three manifolds with boundary. This invariant is often called the twisted Alexander polynomial when we consider li...
Green Currents for Meromorphic Maps of Compact Kahler Manifolds
Green Currents Meromorphic Maps Compact Kahler Manifolds
2011/9/9
Abstract: We consider the dynamics of meromorphic maps of compact K\"ahler manifolds. In this work, our goal is to locate the non-nef locus of invariant classes and provide necessary and sufficient co...
Finite-sided deformation spaces of complete affine 3-manifolds
Finite-sided deformation spaces complete affine 3-manifolds Geometric Topology
2011/9/6
Abstract: A Margulis spacetime is a complete affine 3-manifold M with nonsolvable fundamental group. Associated to every Margulis spacetime is a noncompact complete hyperbolic surface S. We show that ...
Equidistribution of Eisenstein series on convex co-compact hyperbolic manifolds
Equidistribution of Eisenstein series convex co-compact hyperbolic manifolds Spectral Theory
2011/9/5
Abstract: For convex co-compact hyperbolic manifolds $\Gamma\backslash \mathbb{H}^{n+1}$ for which the dimension of the limit set satisfies $\delta_\Gamma< n/2$, we show that the high-frequency Eisens...
Simply Connected Symplectic Calabi-Yau 6-Manifolds
Connected Symplectic Calabi-Yau 6-Manifolds Geometric Topology Algebraic Geometry
2011/9/5
Abstract: In this paper, we construct simply connected symplectic Calabi-Yau 6-manifolds by applying Gompf's symplectic fiber sum operation along $T^4$. Using our construction, we also produce symplec...
Potential Theory on Almost Complex Manifolds
Potential Theory Almost Complex Manifolds Complex Variables
2011/9/5
Abstract: Pseudo-holomorphic curves on almost complex manifolds have been much more intensely studied than their "dual" objects, the plurisubharmonic functions. These functions are defined classically...
Rigidity of high dimensional graph manifolds
Quasi-isometry quasi-action graph of groups CAT(0) space Borel conjecture Baum-Connes conjecture
2011/9/1
Abstract: We define the class of high dimensional graph manifolds. These are compact smooth manifolds supporting a decomposition into finitely many pieces, each of which is diffeomorphic to the produc...
Thin instantons in G_2-manifolds and Seiberg-Witten invariants
G_2-manifolds and Seiberg-Witten invariants Differential Geometry
2011/9/1
Abstract: For two nearby disjoint coassociative submanifolds C and C' in a G_2-manifold, we construct thin instantons with boundaries lying on C and C' from regular J-holomorphic curves in C. We expla...
Voronoi tessellations for matchbox manifolds
Voronoi tessellations Delaunay triangulations almost periodic tilings laminations solenoids matchbox manifolds
2011/9/1
Abstract: Matchbox manifolds ${\mathfrak M}$ are a special class of foliated spaces, which includes as special examples the weak solenoids, and tiling spaces associated to aperiodic tilings with finit...
A tight colored Tverberg theorem for maps to manifolds
colored Tverberg theorem manifolds Combinatorics Algebraic Topology
2011/9/1
Abstract: We prove that any continuous map of an N-dimensional simplex Delta_N with colored vertices to a d-dimensional manifold M must map r points from disjoint rainbow faces of Delta_N to the same ...
Alternating projections on non-tangential manifolds
Alternating projections convergence Non-convexity
2011/9/15
Abstract: We consider sequences $(B_k)_{k=0}^\infty$ of points obtained by projecting back and forth between two manifolds $\M_1$ and $\M_2$, and give conditions guaranteeing that the sequence converg...