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On 1-Harmonic Functions
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2007, том 3
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On 1-Harmonic Functions
Інший ID:
2000 Mathematics Subject Classification: 53C40; 53C42
Посилання:
On 1-Harmonic Functions / S.W. Wei // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 22 назв. — англ.
Підтримка:
This paper is a contribution to the Proceedings of the 2007 Midwest Geometry Conference in honor of Thomas P. Branson. Research was partially supported by NSF Award No DMS-0508661, OU Presidential International Travel Fellowship, and OU Faculty Enrichment Grant. The author wishes to thank Professors H. Blaine Lawson Jr., and Wu-Yi Hsiang for their interest, and Professor Herbert Federer for his help in Theorem 6 which essentially derives from him. The author also wishes to express his gratitude to the referees and the editors for their comments and suggestions without which the present form of this article would not be possible.
Дата:
2007
Переглядів:
550
Завантажень:
169
Анотація:
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.
