6533b831fe1ef96bd1298a59
RESEARCH PRODUCT
Topics in calculus and geometry on metric spaces
Vincenzo Palmisanosubject
quasi-ultrametric spacecalculuCarnot groupconvexityLipschitz functionmetric spaceWhitney type extension theoremextension theoremdoubling spacepartitionSettore MAT/05 - Analisi Matematicasemi-distance distancepaces of homogeneous typequasi-metric spacesmetrization theoremof unity lemmadescription
In this thesis we present an overview of some important known facts related to topology, geometry and calculus on metric spaces. We discuss the well known problem of the existence of a lipschitz equivalent metric to a given quasiultrametric, revisiting known results and counterexamples and providing some new theorems, in an unified approach. Also, in the general setting of a quasi-metric doubling space, suitable partition of unity lemmas allows us to obtain, in step two Carnot groups, the well known Whitney’s extension theorem for a given real function of class C^m defined on a closed subset of the whole space: this result relies on relevant properties of the symmetrized Taylor’s polynomial recently introduced in this setting. Finally, some first interesting investigations on Menger convexity in the setting of a general metric spaces concludes this work.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2022-01-01 |