Biharmonic hypersurfaces in a sphere. (English) Zbl 1366.53046
In [Isr. J. Math. 168, 201–220 (2008; Zbl 1172.58004)], A. Balmus et al. conjectured that every biharmonic submanifold in a sphere has constant mean curvature. In the paper under review, the authors prove a Liouville-type theorem for superharmonic functions on a complete manifold and, as a corollary, they obtain a partial affirmative answer to the above conjecture.
Reviewer: Gabriel Eduard Vilcu (Ploieşti)
MSC:
| 53C43 | Differential geometric aspects of harmonic maps |
| 58E20 | Harmonic maps, etc. |
| 53C40 | Global submanifolds |
Keywords:
biharmonic submanifold; minimal submanifold; Liouville-type theorem; superharmonic function; mean curvatureCitations:
Zbl 1172.58004References:
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