ON THE VOLUME OF (HALF-)TUBULAR NEIGHBORHOODS OF SURFACES IN SUB-RIEMANNIAN GEOMETRY
In 1840 Steiner proved that the volume of the tubular neighborhood of a convex set in R^n is a polynomial of degree n in the size of the tube. The coefficients of such a polynomial carry information about the curvature of the set. In this talk we present Steiner-like formulas in the framework of sub-Riemannian geometry. In particular, we introduce the three-dimensional sub-Riemannian contact manifolds, which the first Heisenberg group is a special case of. Then, we show the asymptotic expansion of the volume of the half-tubular neighborhood of a surface and provide a geometric interpretation of the coefficients in terms of sub-Riemannian curvature objects.