The area minimizing problem in conformal cones, II

Gao, Qiang; Zhou, Hengyu

doi:10.1007/s11425-020-1792-3

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Cited by 3 publications

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“…In the case of translating mean curvature equation (F ≡ 0, φ ≡ c) the Nc-f property can not be removed by a hemisphere example (see [16, section 6]). Some special cases of the Dirichlet problem (1.1) have been studied in [15] and [54] via the area functional approach. For the Dirichlet problem of more general PMC functions, we refer to Bergner's work in [3] with a strict condition on the domain Ω.…”

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confidence: 99%

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A blow-up method to prescribed mean curvature graphs with fixed boundaries

Zhou¹

2022

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In this paper we discuss the existence of prescribed mean curvature (PMC) graphs with fixed graphical boundaries in the product manifold N×R. We define an Nc-f domain in which closure does not contain certain domains with the mean curvature of its boundary equal to f . We show the existence of corresponding PMC graphs over bounded Nc-f domains with natural boundary conditions via a blow-up method from Schoen-Yau. This existence can be used in the Plateau problem of PMC surfaces in 3-manifolds.

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confidence: 99%

“…In what follows we use q(s) denote different continuous functions satisfying q(0) = 0, | q(r) r | ≤ C for all r ∈ [−d 0 , d 0 ] and some positive constant C. Let µ be the constant (A. 16) max…”

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confidence: 99%