Title: Lipschitz Surfaces

Abstract
Extracting topological and/or geometric information about a space given 
just a finite set of points from this space is a hard and, in general, ill 
posed problem. Therefore, we usually try to simplify it by assuming that 
the given set of points and the space under consideration satisfy some 
conditions. It has been shown by N. Amenta and M. Bern that if our space 
is a smooth surface with a positive minimal local feature size and the 
finite set of points is a so-called $\epsilon$-sample, then one can 
recover topological as well as  geometric properties of the surface. Also, 
A. Lieutier and F. Chazal showed that topological properties of the space 
can be recovered under much milder conditions. Recently, J-D. Boissonnant 
and S. Oudot looked at the class of lipschitz surfaces and proved that 
their topology and geometry can be recovered if the given set of points 
satisfies conditions similar to those of an $\epsilon$-sample. In this 
talk I will present the latter result after giving a brief overview of the 
former ones.