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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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2007
Main Author: Wei, S.W.
Format: Article
Language:English
Published: Інститут математики НАН України 2007
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/146897
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:On 1-Harmonic Functions / S.W. Wei // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 22 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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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.
ISSN:1815-0659