Regular Hypersurfaces, Intrinsic Perimeter and Implicit Function Theorem in Carnot Groups
نویسندگان
چکیده
منابع مشابه
Implicit Function Theorem in Carnot–carathéodory Spaces
In this paper, we study the notion of regular surface in the Carnot–Carathéodory spaces and we prove the implicit function theorem in this setting. We fix at every point of R a subset of the tangent space, called horizontal tangent plane, and we assume that it has a basis X1, . . . , Xm of C∞ vector fields satisfying the Hörmander condition of hypoellipticity, (see [16]). This choice induces a ...
متن کاملLocality of the Perimeter in Carnot Groups and Chain Rule
In the class of Carnot groups we study fine properties of sets of finite perimeter. Improving a recent result by Ambrosio-Kleiner-Le Donne, we show that the perimeter measure is local, i.e., that given any pair of sets of finite perimeter their perimeter measures coincide on the intersection of their essential boundaries. This solves a question left open in [4]. As a consequence we prove a gene...
متن کاملImplicit function theorem over free groups
We introduce the notion of a regular quadratic equation and a regular NTQ system over a free group. We prove the results that can be described as Implicit function theorems for algebraic varieties corresponding to regular quadratic and NTQ systems. We will also show that the Implicit function theorem is true only for these varieties. In algebraic geometry such results would be described as lift...
متن کاملThe Implicit Function Theorem and Implicit Parametrizations∗
We discuss a differential equations treatment of the implicit functions problem. Our approach allows a precise and complete description of the solution, of continuity and differentiability properties. The critical case is also considered. The investigation is devoted to dimension two and three, but extensions to higher dimension are possible. MSC: 26B10, 34A12, 53A05. keywords: implicit functio...
متن کاملIsodiametric Inequality in Carnot Groups
The classical isodiametric inequality in the Euclidean space says that balls maximize the volume among all sets with a given diameter. We consider in this paper the case of Carnot groups. We prove that for any Carnot group equipped with a Haar measure one can find a homogeneous distance for which this fails to hold. We also consider Carnot-Carathéodory distances and prove that this also fails f...
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: Communications in Analysis and Geometry
سال: 2003
ISSN: 1019-8385,1944-9992
DOI: 10.4310/cag.2003.v11.n5.a4