[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.2016.53.2.287

ON THE PRESCRIBED MEAN CURVATURE PROBLEM ON THE STANDARD n-DIMENSIONAL BALL

Bensouf, Aymen (Department of Mathematics Faculty of sciences of Gafsa Campus Universitaire)

Publication Information

Journal of the Korean Mathematical Society / v.53, no.2, 2016 , pp. 287-304 More about this Journal

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.

Keywords

boundary mean curvature; variational method; loss of compactness; ${\beta}$ -flatness condition; critical point at infinity;

Citations & Related Records

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