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manuscripta mathematica

, Volume 72, Issue 1, pp 131–140 | Cite as

Hypersurfaces of prescribed mean curvature enclosing a given body

  • Martin Fuchs
Article
  • 37 Downloads

Abstract

Given a smooth domain Ω in ℝ m+1 with compact closure and a smooth integrable functionh: ℝ m+1→ℝ satisfyingh(x)H ∂Ω (x) on ∂Ω whereH ∂ω denotes the mean curvature of ∂Ω calculated w.r.t. the interior unit normal we show that there is a setA⊂ℝ m+1 with the properties\(A \supset \bar \Omega \) andH ∂A=h on ∂A.

Key words

Caccioppoli sets mean curvature closed hypersurfaces 

AMS-classification

49Q20 49F20 49F22 53A10 

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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Martin Fuchs
    • 1
  1. 1.Technische Hochschule DarmstadtDarmstadt

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