Asymptotic analysis of singular solutions of the scalar and mean curvature equations | Zendy

Gonzalo García | Zendy; Hendel Yaker | Zendy

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Asymptotic analysis of singular solutions of the scalar and mean curvature equations

Author(s) -

Gonzalo García,

Hendel Yaker

Publication year - 2005

Publication title -

international journal of mathematics and mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.21

H-Index - 39

eISSN - 1687-0425

pISSN - 0161-1712

DOI - 10.1155/ijmms.2005.679

Subject(s) - mathematics , conformal map , scalar curvature , sobolev space , mathematical analysis , curvature , metric (unit) , scalar (mathematics) , conformal gravity , exponent , pure mathematics , conformal symmetry , geometry , linguistics , operations management , philosophy , economics

We show that positive solutions of a semilinear elliptic problem in the Sobolev critical exponent with Newmann conditions, related to conformal deformation of metrics in ℝ+n, are asymptotically symmetric in a neighborhood of the origin. As a consequence, we prove for a related problem of conformal deformation of metrics in ℝ+n that if a solution satisfies a Kazdan-Warner-type identity, then the conformal metric can be realized as a smooth metric on S+n

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