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

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

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-0013-5D01-2 Version Permalink: https://hdl.handle.net/11858/00-001M-0000-0013-5D02-F
Genre: Journal Article

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 Creators:
Dierkes, Ulrich, Author
Huisken, Gerhard1, Author           
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1Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24012              

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 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.

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 Dates: 1990
 Publication Status: Issued
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 Identifiers: eDoc: 332750
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Title: Pacific Journal of Mathematics
  Alternative Title : PJM
Source Genre: Journal
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Pages: - Volume / Issue: 141 (1) Sequence Number: - Start / End Page: 47 - 54 Identifier: ISSN: 0030-8730