Sub-Riemannian calculus on hypersurfaces in Carnot groups |
| |
Authors: | D Danielli N Garofalo DM Nhieu |
| |
Institution: | a Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA b Department of Mathematics, Georgetown University, Washington, DC 20057-1233, USA |
| |
Abstract: | We develop a sub-Riemannian calculus for hypersurfaces in graded nilpotent Lie groups. We introduce an appropriate geometric framework, such as horizontal Levi-Civita connection, second fundamental form, and horizontal Laplace-Beltrami operator. We analyze the relevant minimal surfaces and prove some basic integration by parts formulas. Using the latter we establish general first and second variation formulas for the horizontal perimeter in the Heisenberg group. Such formulas play a fundamental role in the sub-Riemannian Bernstein problem. |
| |
Keywords: | Horizontal Levi-Civita connection Horizontal second fundamental form H-mean curvature Intrinsic integration by parts First and second variation of the horizontal perimeter |
本文献已被 ScienceDirect 等数据库收录! |
|