Conformal Rigidity and Non-rigidity of the Scalar Curvature on Riemannian Manifolds

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For a compact smooth manifold (M, g(0)) with a boundary, we study the conformal rigidity and non-rigidity of the scalar curvature in the conformal class. It is known that the sign of the first eigenvalue for a linearized operator of the scalar curvature by a conformal change determines the rigidity/non-rigidity of the scalar curvature by conformal changes when the scalar curvature R-g0 is positive. In this paper, we show the sign condition of R-g0 is not necessary, and a reversed rigidity of the scalar curvature in the conformal class does not hold if there exists a point x(0) is an element of M with R-g0 (x(0)) > 0.
Publisher
SPRINGER
Issue Date
2021-10
Language
English
Article Type
Article
Citation

JOURNAL OF GEOMETRIC ANALYSIS, v.31, no.10, pp.9745 - 9767

ISSN
1050-6926
DOI
10.1007/s12220-021-00626-z
URI
http://hdl.handle.net/10203/287549
Appears in Collection
MA-Journal Papers(저널논문)
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