Bi-Lipschitz Characterization of Space Curves
نویسندگان
چکیده
In the paper Targino (Outer Lipschitz Geometry of Complex Algebraic Plane Curves. International Mathematics Research Notices, rnac202. https://doi.org/10.1093/imrn/rnac202 , 2022) Renato shows that bi-Lipschitz type a plane curve is determined by local ambient topological properties curves. Here we show it no longer true in higher dimensions. However space curves number singular points and generic projection such into affine plane.
منابع مشابه
Bi-Lipschitz Decomposition of Lipschitz functions into a Metric space
We prove a quantitative version of the following statement. Given a Lipschitz function f from the k-dimensional unit cube into a general metric space, one can be decomposed f into a finite number of BiLipschitz functions f |Fi so that the k-Hausdorff content of f([0, 1] r ∪Fi) is small. We thus generalize a theorem of P. Jones [Jon88] from the setting of R to the setting of a general metric spa...
متن کاملBi-lipschitz Homogeneous Curves in R Are Quasicircles
We show that a bi-Lipschitz homogeneous curve in the plane must satisfy the bounded turning condition, and that this is false in higher dimensions. Combined with results of Herron and Mayer this gives several characterizations of such curves in the plane.
متن کاملA characterization of curves in Galilean 4-space $G_4$
In the present study, we consider a regular curve in Galilean $4$-space $mathbb{G}_{4}$ whose position vector is written as a linear combination of its Frenet vectors. We characterize such curves in terms of their curvature functions. Further, we obtain some results of rectifying, constant ratio, $T$-constant and $N$-constant curves in $mathbb{G}_{4}$.
متن کاملBi-lipschitz Sufficiency of Jets
We give some theorems of bi-Lipschitz or C sufficiency of jets which are expressed by means of transversality with respect to some strata of a stratification satisfying the (L) condition of T. Mostowski. This enables us to prove that the number of metric types of intersection of smooth transversals to a stratum of an (a) regular stratification of a subanalytic set is finite.
متن کاملLipschitz 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 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: Bulletin Of The Brazilian Mathematical Society, New Series
سال: 2023
ISSN: ['1678-7544', '1678-7714']
DOI: https://doi.org/10.1007/s00574-023-00348-6