Isotropic surface area measures

Surface Area and Other Measures of Ellipsoids

A. We begin by studying the surface area of an ellipsoid in E as the function of the lengths of the semi-axes. We write down an explicit formula as an integral over Sn−1, use this formula to derive convexity properties of the surface area, to give sharp estimates for the surface area of a large-dimensional ellipsoid, to produce asymptotic formulas for the surface area and the isoperimetr...

Volume Inequalities for Isotropic Measures

A direct approach to Ball’s simplex inequality is presented. This approach, which does not use the Brascamp-Lieb inequality, also gives Barthe’s characterization of the simplex for Ball’s inequality and extends it from discrete to arbitrary measures. It also yields the dual inequality, along with equality conditions, and it does both for arbitrary measures. A non-negative Borel measure Z on the...

Isotropic Surface Remeshing

This paper proposes a new method for isotropic remeshing of triangulated surface meshes. Given a triangulated surface mesh to be resampled and a user-specified density function defined over it, we first distribute the desired number of samples by generalizing error diffusion, commonly used in image halftoning, to work directly on mesh triangles and feature edges. We then use the resulting sampl...

Isotropic Surface Remeshing

Stability Results Involving Surface Area Measures of Convex Bodies

We strengthen some known stability results from the Brunn-Minkowski theory and obtain new results of similar types. These results concern pairs of convex bodies for which either surface area measures, or counterparts of such measures in the Brunn-Minkowski-Firey theory, or geometrically significant transforms of such measures, are close to each other. MSC 2000: 52A20, 52A40.