Integrability of the sub-Riemannian mean curvature of surfaces in the Heisenberg group
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- by D. Danielli, N. Garofalo and D. M. Nhieu PDF
- Proc. Amer. Math. Soc. 140 (2012), 811-821 Request permission
Abstract:
The problem of the local summability of the sub-Riemannian mean curvature $\mathcal H$ 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 $\mathcal H$ of a $C^2$ surface $M$ in the Heisenberg group $\mathbb H^1$ in general fails to be integrable with respect to the Riemannian volume on $M$.References
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Additional Information
- D. Danielli
- Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
- MR Author ID: 324114
- Email: danielli@math.purdue.edu
- N. Garofalo
- Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
- MR Author ID: 71535
- Email: garofalo@math.purdue.edu
- D. M. Nhieu
- Affiliation: Department of Mathematics, National Central University, Jhongli City, Taoyuan County 32001, Taiwan, Republic of China
- Email: dmnhieu@math.ncu.edu.tw
- Received by editor(s): August 25, 2010
- Received by editor(s) in revised form: August 31, 2010
- Published electronically: November 2, 2011
- Additional Notes: The first author was supported in part by NSF grant CAREER DMS-0239771
The second author was supported in part by NSF Grant DMS-1001317
The third author was supported in part by NSC Grant 99-2115-M-008-013-MY3 - Communicated by: Mario Bonk
- © Copyright 2011 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 140 (2012), 811-821
- MSC (2010): Primary 49Q05; Secondary 53D10
- DOI: https://doi.org/10.1090/S0002-9939-2011-11058-X
- MathSciNet review: 2869066