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The n-dimensional analogue of the catenary: Prescribed area

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Huisken,  Gerhard
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Citation

Huisken, G., & Dierkes, U. (1996). The n-dimensional analogue of the catenary: Prescribed area. In J. Jost (Ed.), Geometric analysis and the calculus of variations (pp. 1-12). Cambridge: International Press.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-5B74-E
Abstract
We study ”heavy” n–dimensional surfaces which are suspended from some given boundary data ϕ and have prescribed surface area A. Using a fixed point argument we show existence of a solution provided A is close to the area of the corresponding minimal surface spanned by ϕ.