Objective
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)
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
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Programme(s)
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Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Topic(s)
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Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Call for proposal
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Funding Scheme
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Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Coordinator
38402 Saint-Martin-d'Hères
France
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