منابع مشابه
Lipschitz Geometry of Complex Curves
We describe the Lipschitz geometry of complex curves. For the most part this is well known material, but we give a stronger version even of known results. In particular, we give a quick proof, without any analytic restrictions, that the outer Lipschitz geometry of a germ of a complex plane curve determines and is determined by its embedded topology. This was first proved by Pham and Teissier, b...
متن کاملLipschitz Geometry of Complex Surfaces: Analytic Invariants and Equisingularity
We prove that the outer Lipschitz geometry of the germ of a normal complex surface singularity determines a large amount of its analytic structure. In particular, it follows that any analytic family of normal surface singularities with constant Lipschitz geometry is Zariski equisingular. We also prove a strong converse for families of normal complex hypersurface singularities in C3: Zariski equ...
متن کاملGeometry of Lipschitz Percolation
We prove several facts concerning Lipschitz percolation, including the following. The critical probability pL for the existence of an open Lipschitz surface in site percolation on Z with d ≥ 2 satisfies the improved bound pL ≤ 1−1/[8(d−1)]. Whenever p > pL, the height of the lowest Lipschitz surface above the origin has an exponentially decaying tail. For p sufficiently close to 1, the connecte...
متن کاملGeometry of the Complex of Curves and of Teichmüller Space
Using train tracks on a non-exceptional oriented surface S of finite type in a systematic way we give a proof that the complex of curves C(S) of S is a hyperbolic geodesic metric space. We also discuss the relation between the geometry of the complex of curves and the geometry of Teichmüller space.
متن کاملGeometry of the Complex of Curves Ii: Hierarchical Structure
In this paper we continue our geometric study of Harvey’s Complex of Curves [12], a finite dimensional and locally infinite complex C(S) associated to a surface S, which admits an action by the mapping class group Mod(S). The geometry and combinatorics of C(S) can be applied to study grouptheoretic properties of Mod(S), and the geometry of Kleinian representations of π1(S). In [19] we showed th...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Singularities
سال: 2014
ISSN: 1949-2006
DOI: 10.5427/jsing.2014.10o