Minimal entropy and topological rigidity of manifolds admitting nontrivial maps onto locally symmetric spaces
4РП — Обучение и мобилност на изследователи
- Период
- 1998-07-06 → 1999-07-05
- Финансиране от ЕС
- —
- Участници
- 1
- Схема
- RGI
Линиите свързват координатора с партньорите. За проекти отпреди 2014 г. CORDIS не винаги дава точни координати. Тези точки са на ниво град или държава.
Накратко на български
Геометричните свойства на многомерни пространства, като например кривината им, се анализират чрез връзката между обема и ентропията. Това помага да се разбере как формата на едно пространство ограничава неговата структура и топологична гъвкавост.
Кратко обяснение, генерирано от езиков модел по текста на CORDIS. Оригиналът е по-долу.
Цел на проекта
RESEARCH OBJECTIVES AND CONTENT The objective of the project is to investigate certain problems of topological and differential rigidity related to the Minimal Entropy Problem, for manifolds admitting nontrivial maps onto locally symmetric spaces of negative curvature. I am going especially to treat the case of negatively curved manifolds and that of manifolds with splittable fundamental group. With this aim, I intend to study the notion of growth tightness in Riemannian Geometry, which seems to play a crucial role in such problems. I also mean to analyze the relationship between the pinching of the volume-entropy functional (possibly under additional assumptions on the geometric invariants of the metrics realizing the pinching) and the Gromov-Hausdorff convergence. TRAINING CONTENT (OBJECTIVE, BENEFIT AND EXPECTED IMPACT) The training content concerns the study of the most recent techniques developed to deal with these topics, namely: - approximation of isometries by means of immersions in spaces of measures, following Besson-Courtois-Gallot; - Gromov hyperbolic groups; - methods a la Cheeger-Colding for manifolds with Ricci curvature bounded from below (Gromov-Hausdorff distance, Bochner formulas, approximation of distance functions with harmonic functions). The combination of the above mentioned techniques should lead to a new approach to the investigation of pinching problems and of rigidity of negatively curved manifolds. Links with industry / industrial relevance (22)
Оригинален текст от CORDIS (на английски).
Участници
- Université de Grenoble I (Université Joseph Fourier) · Saint-Martin-d'HèresКоординаторНиво градФранция
Връзки
Данни: CORDIS, © Европейски съюз