NADITIDIBAS · Nonlinear analysis and differential topology in infinite dimensional Banach spaces
6РП — Действия „Мария Кюри“
- Период
- 2004-02-15 → 2005-07-14
- Финансиране от ЕС
- 102 756 €
- Участници
- 1
- Схема
- EIF
Линиите свързват координатора с партньорите.
Накратко на български
Математическите свойства на функции и уравнения върху криволинейни повърхности, наречени Риманови многообразия, се анализират чрез нови формули и теореми. Тези инструменти помагат за по-точното описание на сложни геометрични пространства и промените в тях.
Кратко обяснение, генерирано от езиков модел по текста на CORDIS. Оригиналът е по-долу.
Резултати накратко
Final Activity Report Summary - NADITIDIBAS (Nonlinear analysis and differential topology in infinite dimensional Banach spaces)
As a result of this project the following were achieved: A new maximum principle was obtained for viscosity subsolutions and supersolutions of evolution equations on a Riemannian manifold with some weak restrictions. A new notion of proximal gradient was introduced for functions defined on Riemannian manifold and a nonsmooth calculus (in the sense of Clarke) was developed for this new notion. Several new fixed point theorems were obtained, concerning expansive and nonexpansive mappings on a (possibly non compact) Riemannian manifold and their small perturbations. New regularisation results were obtained for convex functions defined on Riemannian manifolds with negative sectional curvature (by generalizing Moreau's inf-convolution procedure in this context).
Текст от CORDIS, на английски · Данни: CORDIS, © Европейски съюз
Цел на проекта
Until now, I have worked mainly on smoothness and geometrical properties of Banish spaces and their interplay with infinite-dimensional differential topology. For instance, I have shown inky thesis that every smooth sphere (note that we say the whole sphere and not the sphere minus a point) in any infinite-dimensional Banish space is diffeomorphic to a hyper plane, thus providing a full generalization of a celebrated result of Messages. We have also established Avery strong approximate form of the Morse-Surd theorem, which holds in every differentiable manifold modelled on an infinite-dimensional Hubert space. The two main objectives of the project are1) to continue research in the topic explained above, which is also one of the areas of speciality of Professor Gilles Godefory; and2) to tyro expand my research into new directions such as the study of linear operators, invariant subspace problems and hyper cyclic operators, which are all among the fields of expertise of Professors Gilles Gaudery and Gilles Pismire, both working at the Institute de Mathématiques departs 6. I think that I could learn a lot of things from them and from their research teams, which would be extremely useful for me to develop my research in these directions. On the other hand, the Institute de Mathématiques de Paris 6 is one of the best centres of Mathematics in Europe, and the opportunity of interacting and working with its members would have a very positive impact on my postdoctoral training as a mathematician and would contribute to launch out my research activities into the new fields that I would like to explore.
Оригинален текст от CORDIS (на английски).
Участници
- UNIVERSITE PIERRE ET MARIE CURIE · PARISКоординаторФранция
Връзки
Данни: CORDIS, © Европейски съюз