Séminaire de Géométrie, Groupes et Dynamique
# Marcos Cossarini: "Discrete Metric Geometry"

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435 (UMPA)
### 435

#### UMPA

Description

A wallsystem on a manifold is a codimension-1 submanifold satisfying certain conditions. It allows us to define a discrete notion of length and volume: the length of a curve in the manifold is the number of times that it crosses the wallsystem, and the volume of the manifold (of dimension n) is the number of self-intersections of order n of the wallsystem. We will see how to approximate any Riemannian metric on a compact manifold by a wallsystem, and we'll discuss applications to the filling area problem and the inverse problem for boundary distances.