Erwin Schrödinger Fellowship J 1961 Asymptotic approximation of convex bodies Monika LUDWIG 26.6.2000
During my stay at the Polytechnic University New York I want to work jointly with my colleagues on the
following questions:
1) Approximation of convex bodies and
2) Characterization of valuations on the space of convex bodies
Both subjects are central questions within convex geometry, a part of mathematics situated between geometry and
analysis. The first question is to approximate a convex set as well as possible by polyhedra. Problems of
approximation generally and especially problems of polyhedral and spline approximation of surfaces are important
for many applications, e.g., Computer Aided Design and modern computer geometry. Valuations are a very useful
tool in
many areas of geometry, e.g., integral geometry. The aim of the project is to find applications of results on
characterizations of valuations to problems of approximation.