On a class of locally conformally flat manifolds

By S. Chang, Fengbo Hang, Paul Yang. 2004

64 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology, Health, Toxicology and Mutagenesis

View Paper: https://www.semanticscholar.org/paper/13c26425675000f628a5690958ad34ca3db01687

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In Applied Mathematics

In Geometry and Topology

In Health, Toxicology and Mutagenesis

María del Mar González

Citations in the corpus

Classification of singular radial solutions to the σk Yamabe equation on annular domains (2005, unknown): “In fact, in [8], Chang, Hang, and Yang proved that if Ω ⊂ S (n ≥ 5) admits a complete, conformal metric g with σ1(Ag) ≥ c1 > 0, σ2(Ag) ≥ 0, and |Rg| + |∇gR|g ≤ c0, (2) then dim(S \ Ω) < n−4 2 .”
Schouten tensor and some topological properties (2005, unknown): “After this paper was completed, we learned two recent papers by Chang-Hang-Yang [2] and González [3] on further topological implications of Γk positivity for locally conformally flat manifolds.”
Singular sets of a class of locally conformally flat manifolds (2005, methodology): “The proof is based on the case k = 2 (covered by Chang-Hang-Yang in [5]), and the inductive formula developed in section 4.”
Asymptotic Expansions of Solutions of the Yamabe Equation and the σk‐Yamabe Equation near Isolated Singular Points (2019, background): “Refer to [10] and references there for more information concerning the σk-Yamabe equation, and in particular to [4], [6], and [7] for the size of the singular sets, and to [16] and [17] for the existence of solutions with isolated singularity.”
Asymptotic behavior of solutions to the σk-Yamabe equation near isolated singularities (2009, unknown): “In fact, in [18], Chang, Hang, and Yang proved that if ⊂ S (n ≥ 5) admits a complete, conformal metric g with σ1(Ag) ≥ c1 > 0, σ2(Ag) ≥ 0, and |Rg| + |∇gR|g ≤ c0, (9) then dim(S \ ) < (n − 4)/2.”
Singular Solutions of Fractional Order Conformal Laplacians (2009, background): “for the standard Q−curvature, this result is already known: it is shown in [4] that complete metrics with Q2 > 0 and positive scalar curvature must have singular set with dimension less than (n− 4)/2, which again agrees with (1.”