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Fractal curvature measures and Minkowski content for one-dimensional self-conformal sets
Fractal curvature measures Minkowski one-dimensional self-conformal sets
2011/2/28
We investigate intrinsic geometric properties of invariant sets of one-dimensional conformal iterated function systems. We show that for such a set F the fractal cur-vature measures exist, if and only...
Flippable tilings of constant curvature surfaces
Flippable tilings constant curvature surfaces
2011/1/19
We call “flippable tilings” of a constant curvature surface a tiling by “black” and “white” faces, so that each edge is adjacent to two black and two white faces (one of each on each side), the black ...
On the singular set of mean curvature flows with Neumann free boundary conditions
singular set of mean curvature flows Neumann free boundary conditions
2011/1/17
We consider n-dimensional hypersurfaces flowing by mean curvature flow with Neumann free
boundary conditions supported on a smooth support surface. We show that the Hausdorff n-measure of the singula...
To a function with values in the power set of a pre–ordered, separated locally convex space a family of scalarizations is given which completely characterizes the original function.A concept of a Lege...
We show that projective K3 surfaces with odd Picard rank contain infinitely many rational curves. Our proof extends the Bogomolov-Hassett-Tschinkel approach, i.e., uses moduli spaces of stable maps an...
Microlocal analysis of asymptotically hyperbolic and Kerr-de Sitter spaces
Microlocal analysis asymptotically hyperbolic Kerr-de Sitter spaces
2011/2/24
In this paper we develop a general, systematic, microlocal framework for the Fredholm analysis of non-elliptic problems, including high energy (or semiclassical) estimates, which is stable under pertu...
Let V be a discrete valuation ring of mixed characteristic with perfect residue field. Let
X be a geometrically connected smooth proper curve over V.
Counting Essential Surfaces in a Closed Hyperbolic 3-Manifold
Counting Essential Surfaces Closed Hyperbolic 3-Manifold
2011/1/21
Let M3 be a closed hyperbolic three manifold. We show that the number of genus g surface subgroups of 1(M3) grows like g 2g.
On the abundance of non-zero central Lyapunov exponents, physical measures and stable ergodicity for partially hyperbolic dynamics
u-Gibbs states physical measures partially hyperbolic dynamics minimal foliations
2011/1/20
We show that each strongly partially hyperbolic C2 diffeomorphism, with one-dimensional subbundles and C2 smooth andminimal strong-unstable foliation, is C2 close to a diffeomorphism having non-zero c...
Growth of Weil-Petersson volumes and random hyperbolic surfaces of large genus
Growth of Weil-Petersson volumes random hyperbolic surfaces of large genus
2011/1/20
In this paper, we investigate the geometric properties of hyperbolic surfaces by studying the lengths of simple closed geodesics. The moduli space Mg,n of complete hyperbolic surfaces of genus g ≥ 2 w...
On a General Linear Nonlocal Curvature Flow of Convex Plane Curves
General Linear Nonlocal Curvature Flow Convex Plane Curves
2011/1/17
Motivated by Pan-Yang [PY] and Ma-Cheng [MC], we study a general linear nonlocal cur-vature flow for convex closed plane curves and discuss the short time existence and asymptotic
convergence behavio...
Relative Node Polynomials for Plane Curves
Enumerative geometry floor diagram Gromov-Witten theory
2010/12/13
We generalize the recent work of S. Fomin and G. Mikhalkin on polynomial formulas for Severi degrees.
Hyperbolic surface subgroups of one-ended doubles of free groups
hyperbolic group surface group diskbusting polygonality
2010/12/9
Gromov asked whether every one-ended word-hyperbolic group contains a hyperbolic surface group. We prove that every one-ended double of a free group contains a hyperbolic surface
group if the free gr...
Traveling plateaus for a hyperbolic Keller-Segel system with attraction and repulsion: existence and branching instabilities
Keller-Segel system hyperbolic system traveling waves branching instability
2010/12/16
How can repulsive and attractive forces, acting on a conservative system, create stable traveling patterns or branching instabilities? We have proposed to study this question in the framework of the h...
Lawson's genus two minimal surface and meromorphic connections
Lawson's genus two minimal surface meromorphic connections
2010/12/14
We investigate the Lawson genus 2 surface by methods from integrable system theory. We prove that the associated family of flat connections comes from a family of flat connections on a 4−punctur...