Topological arguments in prescribing the scalar curvature under minimal boundary mean curvature condition on \(S^{n}_{+}\). (English) Zbl 1224.18012

Summary: This paper is devoted to the prescribed scalar curvature problem under minimal boundary mean curvature condition on the standard \(n\)-dimensional half sphere with \(n\geq 3\). Using tools related to the theory of critical points at infinity, we provide some topological conditions, on the level sets of a given positive function on \(S^{n}_{+}\), under which we prove some existence results.


18G35 Chain complexes (category-theoretic aspects), dg categories
35J61 Semilinear elliptic equations
35J25 Boundary value problems for second-order elliptic equations
57R58 Floer homology
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces