Chennai Mathematical Institute


M.Sc. Thesis Defence
11:30 am-12:30 pm, Lecture Hall 5
Sets with Positive Reach

Gautam Aishwarya
M.Sc. Mathematics, Chennai Mathematical Institute.


In this talk we shall discuss the dependency of the volume of tubes around a fixed subset of Euclidean space on the width of the tube. J. Steiner showed that this dependency is a polynomial relation when the subset fixed is compact and convex. Similar dependency was discovered by H. Weyl in context of compact C2-submanifolds when the thickness of tubes is restricted to sufficiently small values. Our central theme shall be H. Federer's approach to this problem, in which one abstracts the exact property of these sets (namely reach) which makes such a polynomial expression possible, and the preceding discoveries are generalised to a larger class of sets called Sets with Positive Reach. We shall also review the prerequisites during the talk.