Volume of the epsilon neighborhood of a submanifold isometrically embedded in R^N
Event details
| Date | 20.05.2014 |
| Hour | 16:15 › 17:15 |
| Speaker | Adrien Marcone (EPFL) |
| Location | |
| Category | Conferences - Seminars |
Geometry and Dynamics Seminar
Abstract: The talk is concerned with the volume of the epsilon neighbourhood of an isometrically embedded submanifold in R^N. First I will discuss the Steiner formula for convex compact subsets of R^n. This formula states that the volume of the epsilon neighbourhood of a convex compact set K in R^N is a polynomial in epsilon whose coefficients are the so-called Quermassintegrals of Minkowski.
After that, I will talk about Weyl's tube formula, which is a kind of generalization of the Steiner formula. Weyl proved in 1939 that if M is a compact submanifold isometrically embedded in R^N then the volume of the epsilon neighbourhood is also a polynomial in epsilon whose coefficients are called the Lipschitz-Killing curvatures and those only depend on the curvature tensor of M. In particular, this implies that the volume of this epsilon neighbourhood does not depend on the way the submanifold is embedded in the ambiant space.
The talk is based on my Master thesis.
Abstract: The talk is concerned with the volume of the epsilon neighbourhood of an isometrically embedded submanifold in R^N. First I will discuss the Steiner formula for convex compact subsets of R^n. This formula states that the volume of the epsilon neighbourhood of a convex compact set K in R^N is a polynomial in epsilon whose coefficients are the so-called Quermassintegrals of Minkowski.
After that, I will talk about Weyl's tube formula, which is a kind of generalization of the Steiner formula. Weyl proved in 1939 that if M is a compact submanifold isometrically embedded in R^N then the volume of the epsilon neighbourhood is also a polynomial in epsilon whose coefficients are called the Lipschitz-Killing curvatures and those only depend on the curvature tensor of M. In particular, this implies that the volume of this epsilon neighbourhood does not depend on the way the submanifold is embedded in the ambiant space.
The talk is based on my Master thesis.
Practical information
- Expert
- Free
Organizer
- Martins Bruveris
Contact
- martins.bruveris@epfl.ch