Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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ON THE PRESCRIBED MEAN CURVATURE PROBLEM ON THE STANDARD n-DIMENSIONAL BALL

  • Bensouf, Aymen (Department of Mathematics Faculty of sciences of Gafsa Campus Universitaire)
  • Received : 2014.11.23
  • Published : 2016.03.01
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Abstract

In this paper, we consider the problem of existence of conformal metrics with prescribed mean curvature on the unit ball of ${\mathbb{R}}^n$, $n{\geq}3$. Under the assumption that the order of flatness at critical points of prescribed mean curvature function H(x) is ${\beta}{\in}[1,n-2]$, we give precise estimates on the losses of the compactness and we prove new existence result through an Euler-Hopf type formula.

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References

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