Kinematic formula and tube formula in space of constant curvature

A Gaussian Kinematic Formula

In this paper, we consider smooth, real-valued random fields built up from i.i.d. copies of centered, unit variance smooth Gaussian fields on a manifold M . Specifically, we consider random fields of the form fp = F (y1(p), . . . , yk(p)) for F ∈ C(R;R) and (y1, . . . , yk) a vector of C centered, unit-variance Gaussian fields. For fields of this type, we compute the expected Euler characterist...

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

The Kinematic Formula in Riemannian Homogeneous Spaces

Let G be a Lie group and K a compact subgroup of G. Then the homogeneous space G/K has an invariant Riemannian metric and an invariant volume form ΩG. Let M and N be compact submanifolds of G/K, and I(M ∩ gN) an “integral invariant” of the intersection M ∩ gN . Then the integral

Robustness of Tube Formula Based Conndence Bands

Simultaneous conndence bands of a regression curve may be used to quantify the uncertainty of an estimate of the curve. The tube formula for volumes of tubular neighborhoods of a manifold provides a very powerful method for obtaining such bands at a prescribed level, when errors are Gaussian. This paper studies robustness of the tube formula for non-Gaussian errors. The formula holds without mo...

Curvature Estimation over Smooth Polygonal Meshes Using the Half Tube Formula

The interest, in recent years, in the geometric processing of polygonal meshes, has spawned a whole range of algorithms to estimate curvature properties over smooth polygonal meshes. Being a discrete approximation of a C continuous surface, these methods attempt to estimate the curvature properties of the original surface. The best known methods are quite effective in estimating the total or Ga...