Geometric measure theory could answer long-standing open problems in mathematics
The aim of the EU-funded STMAGMT project is to lay theoretical foundations in different areas of geometric measure theory to answer fundamental questions that relate to modern mathematical analysis. The project will expand on newly developed geometric measure theory techniques that address arbitrary metric spaces to solve seemingly unrelated problems in different fields of mathematical analysis, such as the calculus of variations, harmonic analysis and geometric function theory, and differential geometry. The project will concentrate on three main objectives: generalising classical characterisations of rectifiability to non-Euclidean settings; proving a quantitative analogue to the Besicovitch-Federer projection theorem; and solving the flat chain conjecture of Ambrosio and Kirchheim.
Funding SchemeERC-STG - Starting Grant
CV4 8UW Coventry
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