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Journal Article

The $n$-dimensional analogue of the catenary: existence and nonexistence

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

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Citation

Dierkes, U., & Huisken, G. (1990). The $n$-dimensional analogue of the catenary: existence and nonexistence. Pacific Journal of Mathematics, 141(1), 47-54.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-5D01-2
Abstract
We study "heavy" A?-dimensional surfaces suspended from some prescribed (n — 1) -dimensional boundary data. This leads to a mean curvature type equation with a non-monotone right hand side. We show that the equation has no solution if the boundary data are too small, and, using a fixed point argument, that the problem always has a smooth solution for sufficiently large boundary data.