Invariance of regularity conditions under definable, locally Lipschitz, weakly bi-Lipschitz mappings
نویسندگان
چکیده
منابع مشابه
2 00 9 Invariance of Regularity Conditions under Definable , Locally Lipschitz , Weakly Bi - Lipschitz Mappings
In this paper we describe the notion of a weak lipschitzianity of a mapping on a C stratification. We also distinguish a class of regularity conditions that are in some sense invariant under definable, locally Lipschitz and weakly bi-Lipschitz homeomorphisms. This class includes the Whitney (B) condition and the Verdier condition.
متن کاملBi-Lipschitz Mappings and Quasinearly Subharmonic Functions
After considering a variant of the generalized mean value inequality of quasinearly subharmonic functions, we consider certain invariance properties of quasinearly subharmonic functions. Kojić has shown that in the plane case both the class of quasinearly subharmonic functions and the class of regularly oscillating functions are invariant under conformal mappings. We give partial generalization...
متن کاملAmenability, Locally Finite Spaces, and Bi-lipschitz Embeddings
We define the isoperimetric constant for any locally finite metric space and we study the property of having isoperimetric constant equal to zero. This property, called Small Neighborhood property, clearly extends amenability to any locally finite space. Therefore, we start making a comparison between this property and other notions of amenability for locally finite metric spaces that have been...
متن کاملDefinable Smoothing of Lipschitz Continuous Functions
Let M be an o-minimal structure over the real closed field R. We prove the definable smoothing of definable Lipschitz continuous functions. In the case of Lipschitz functions of one variable we are even able to preserve the Lipschitz constant.
متن کاملBi-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 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: Annales Polonici Mathematici
سال: 2010
ISSN: 0066-2216,1730-6272
DOI: 10.4064/ap97-1-1