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On the prescribed scalar curvature problem on the three-dimensional half sphere. (English) Zbl 1197.53081

Summary: We provide a variety of classes of functions that can be realized as the scalar curvature of the standard three-dimensional half sphere with respect to some metric whose boundary mean curvature is zero. Such a problem is nontrivial, since we have to overcome topological obstructions.

MSC:

53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010)
35J60 Nonlinear elliptic equations
35J65 Nonlinear boundary value problems for linear elliptic equations
35J93 Quasilinear elliptic equations with mean curvature operator
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