Prescribed mean curvature equation on torus
Keyword(s):
Abstract Prescribed mean curvature problems on the torus have been considered in one dimension. In this paper, we prove the existence of a graph on the n-dimensional torus 𝕋 n {\mathbb{T}^{n}} , the mean curvature vector of which equals the normal component of a given vector field satisfying suitable conditions for a Sobolev norm, the integrated value, and monotonicity.
2007 ◽
Vol 241
(1)
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pp. 112-129
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2017 ◽
Vol 24
(1)
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pp. 113-134
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2003 ◽
Vol 52
(4)
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pp. 1069-1077
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2019 ◽
Vol 21
(03)
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pp. 1850003
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2010 ◽
Vol 21
(4)
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pp. 982-1035
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