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On 1-Harmonic Functions
Characterizations of entire subsolutions for the 1-harmonic equation of a constant 1-tension field are given with applications in geometry via transformation group theory. In particular, we prove that every level hypersurface of such a subsolution is calibrated and hence is area-minimizing over R; a...
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2007
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/146897 |
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| Summary: | Characterizations of entire subsolutions for the 1-harmonic equation of a constant 1-tension field are given with applications in geometry via transformation group theory. In particular, we prove that every level hypersurface of such a subsolution is calibrated and hence is area-minimizing over R; and every 7-dimensional SO(2) × SO(6)-invariant absolutely area-minimizing integral current in R8 is real analytic. The assumption on the SO(2) × SO(6)-invariance cannot be removed, due to the first counter-example in R8, proved by Bombieri, De Girogi and Giusti. |
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