Anisotropic tubular neighborhoods of sets

Inference of curvature using tubular neighborhoods

Effective Dynamics on Small Tubular Neighborhoods

The effective dynamic of a quantum particle on the tubular neighbourhood of some closed submanifold of a riemannian manifold can be described by an effective dynamic on the submanifold as the diameter of the tube decreases to zero. It depends whether Dirichletor Neumann conditions are imposed at the boundary of the tube.

Se p 20 05 MOTIVIC TUBULAR NEIGHBORHOODS

We construct motivic versions of the classical tubular neighborhood and the punctured tubular neighborhood, and give applications to the construction of tangential base-points for mixed Tate motives, algebraic gluing of curves with boundary components , and limit motives.

On the Volume of Tubular Neighborhoods of Real Algebraic Varieties

The problem of determining the volume of a tubular neighborhood has a long and rich history. Bounds on the volume of neighborhoods of algebraic sets have turned out to play an important role in the probabilistic analysis of condition numbers in numerical analysis. We present a self-contained derivation of bounds on the probability that a random point, chosen uniformly from a ball, lies within a...

Smooth Homogenization of Heat Equations on Tubular Neighborhoods

We consider the heat equation with Dirichlet boundary conditions on the tubular neighborhood of a closed Riemannian submanifold of a Riemannian manifold. We show that, as the tube diameter tends to zero, a suitably rescaled and renormalized semigroup converges to a limit semigroup in Sobolev spaces of arbitrarily large Sobolev index.