Infinitesimal Structure of Differentiability Spaces, and Metric Differentiation
نویسندگان
چکیده
منابع مشابه
Infinitesimal Structure of Differentiability Spaces, and Metric Differentiation
We prove metric differentiation for differentiability spaces in the sense of Cheeger [Che99, Kei04a, Bat12]. As corollaries we give a new proof of one of the main results of [Che99], a proof that the Lip-lip constant of any Liplip space in the sense of Keith [Kei04a] is equal to 1, and new nonembeddability results.
متن کاملOn the Structure of Metric-like Spaces
The main purpose of this paper is to introduce several concepts of the metric-like spaces. For instance, we define concepts such as equal-like points, cluster points and completely separate points. Furthermore, this paper is an attempt to present compatibility definitions for the distance between a point and a subset of a metric-like space and also for the distance between two subsets of a metr...
متن کاملExistence and Differentiability of Metric Projections in Hilbert Spaces
This paper considers metric projections onto a closed subset S of a Hilbert space. If the set S is convex, then it is well known that the corresponding metric projections always exist, unique and directionally differentiable at boundary points of S. These properties of metric projections are considered for possibly nonconvex sets S. In particular, existence and directional differentiability of ...
متن کاملDIFFERENTIABILITY OF p-HARMONIC FUNCTIONS ON METRIC MEASURE SPACES
We study p-harmonic functions on metric measure spaces, which are formulated as minimizers to certain energy functionals. For spaces supporting a p-Poincaré inequality, we show that such functions satisfy an infinitesmal Lipschitz condition almost everywhere. This result is essentially sharp, since there are examples of metric spaces and p-harmonic functions that fail to be locally Lipschitz co...
متن کاملOn Φ-differentiability of Functions over Metric Spaces
In 1933 S. Mazur [4] proved the following Theorem 1. Let (X, ·) be a separable real Banach space. Let f be a real-valued convex continuous function defined on an open convex subset Ω ⊂ X. Then there is a subset A ⊂ Ω of the first category such that f is Gateaux differentiable on Ω \ A. The result of Mazur was a starting point for the theory of differentiability of convex functions (cf. the book...
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: Analysis and Geometry in Metric Spaces
سال: 2016
ISSN: 2299-3274
DOI: 10.1515/agms-2016-0005