摘要
The problem of the local summability of the sub-Riemannian mean curvature H of a hypersurface M in the Heisenberg group, or in more general Carnot groups, near the characteristic set of M arises naturally in several questions in geometric measure theory. We construct an example which shows that the sub-Riemannian mean curvature H of a C2 surface M in the Heisenberg group H1 in general fails to be integrable with respect to the Riemannian volume on M.
原文 | ???core.languages.en_GB??? |
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頁(從 - 到) | 811-821 |
頁數 | 11 |
期刊 | Proceedings of the American Mathematical Society |
卷 | 140 |
發行號 | 3 |
DOIs | |
出版狀態 | 已出版 - 2012 |