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ON THE Lr-OPERATORS PENALIZED BY (r + 1)-MEAN CURVATURE.
- Source :
-
Proceedings of the American Mathematical Society . Sep2018, Vol. 146 Issue 9, p4021-4027. 7p. - Publication Year :
- 2018
-
Abstract
- In this paper, we establish the non-positivity of the second eigenvalue of the Schrödinger operator-div(Pr ∇ ·)-Wr² on a closed hypersurface Σn of ℝn+1, where Wr is a power of the (r + 1)-th mean curvature of Σn, which we will ask to be positive. If this eigenvalue is null, we will have a characterization of the sphere. This theorem generalizes the result of Harrell and Loss proved to the Laplace-Beltrame operator penalized by the square of the mean curvature. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00029939
- Volume :
- 146
- Issue :
- 9
- Database :
- Academic Search Index
- Journal :
- Proceedings of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 130701277
- Full Text :
- https://doi.org/10.1090/proc/14098