A bridge between Geometric Measure and Discrete Surface Theories – GeMfaceT

This project positions at the interface between geometric measure and discrete surface theories. There has recently been a growing interest in non-smooth structures, both from theoretical point of view, where singularities occur in famous optimization problems such as Plateau problem or geometric flows such as mean curvature flow, and applied point of view where complex high dimensional data are no longer assumed to lie on a smooth manifold but are more singular and allow crossings, tree-structures and dimension variations. We propose in this project to strengthen and expand the use of geometric measure concepts in discrete surface study and complex data modelling and also, to use those possible singular disrcete surfaces to compute numerical solutions to the aforementioned problems.