紹介
This book gives an up-to-date account of progress on Pansu's celebrated problem on the sub-Riemannian isoperimetric profile of the Heisenberg group. It also serves as an introduction to the general field of sub-Riemannian geometric analysis. It develops the methods and tools of sub-Riemannian differential geometry, nonsmooth analysis, and geometric measure theory suitable for attacks on Pansu's problem.
目次
The Isoperimetric Problem in Euclidean Space.- The Heisenberg Group and Sub-Riemannian Geometry.- Applications of Heisenberg Geometry.- Horizontal Geometry of Submanifolds.- Sobolev and BV Spaces.- Geometric Measure Theory and Geometric Function Theory.- The Isoperimetric Inequality in ?.- The Isoperimetric Profile of ?.- Best Constants for Other Geometric Inequalities on the Heisenberg Group.
