NONLINEAR QUOTIENTS · Nonlinear quotients and geometry of banach spaces
FP6 — Marie Curie Actions (Human Resources and Mobility)
- Duration
- 2003-12-01 → 2005-11-30
- EU contribution
- €163,696
- Participants
- 1
- Scheme
- EIF
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Results in brief
Final Activity Report Summary - NONLINEAR QUOTIENTS (Nonlinear Quotients and Geometry of Banach Spaces)
For my purposes it is important to understand the geometric structure of various deformations and transformations. (An obvious example, that is mildly connected with this research, is in elasticity.) Various classes of such deformations that correspond to different geometric situations were studied in the framework of this project, for example, Lipschitz functions, Lipschitz quotients, uniform co-Lipschitz functions and ball non collapsing functions. The key problem of the study of the local behaviour is whether deformations look like affine ones close to some points, or even close to many points; the relevant classes of exceptional points studied in this project were, for example, cone null sets, regularly cone null sets and sigma-porous sets. The main results include an invariance theorem for cone null and regularly cone null sets under bi-Lipschitz isomorphisms, a construction of unexpectedly large sigma-porous sets in metric spaces admitting certain Lipschitz quotients and a study of a non-linear version of the Besicovitch-Federer projection theorem. These results are relevant especially for future development of geometric non-linear functional analysis and neighbouring fields.
Data: CORDIS, © European Union
Project objective
It is proposed to study a number of the open questions in the general area of non-linear geometric functional analysis. The research in this area involves a rich interplay between classical analysis, geometry of Banach spaces, geometric measure theory, topology and combinatorics.Some of the specific questions we would wish to consider are:- Lower bounds for the volume ratios of Lipschitz quotient mappings.- Gorelik principle for Lipschitz quotient mappings with constants close to one.- Quas irregularity of Lipschitz quotient mappings between spaces of the same (finite) dimension.- Linearisation of Lipschitz mappings, in particular in infinite dimensional spaces.The applicant's work to date has contributed to the first two topics. The proposed work would thus continue this earlier work in a logical fashion, and also extend it into related areas which are currently very active. A major objective of the proposed research is to extend and diversify the applicant's fields of expertise, by allowing her the opportunity to collaborate with one of the most active groups of mathematicians working in her area.
Original text from CORDIS.
Participants
- UNIVERSITY COLLEGE LONDON · LONDONCoordinatorUnited Kingdom
Links
Data: CORDIS, © European Union