Sub-Riemannian calculus on hypersurfaces in Carnot groups

D. Danielli, N. Garofalo, D. M. Nhieu

研究成果: 雜誌貢獻期刊論文同行評審

74 引文 斯高帕斯(Scopus)

摘要

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.

原文???core.languages.en_GB???
頁(從 - 到)292-378
頁數87
期刊Advances in Mathematics
215
發行號1
DOIs
出版狀態已出版 - 20 10月 2007

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