scholarly journals THREE DIMENSIONAL CRITICAL POINT OF THE TOTAL SCALAR CURVATURE

2013 ◽  
Vol 50 (3) ◽  
pp. 867-871 ◽  
Author(s):  
Seungsu Hwang
Keyword(s):  
Scalar Curvature ◽  
Critical Point ◽  
Three Dimensional ◽  
Total Scalar Curvature

scholarly journals CRITICAL POINT METRICS OF THE TOTAL SCALAR CURVATURE

2012 ◽  
Vol 49 (3) ◽  
pp. 655-667 ◽  
Author(s):  
Jeong-Wook Chang ◽  
Seung-Su Hwang ◽  
Gab-Jin Yun
Keyword(s):  
Scalar Curvature ◽  
Critical Point ◽  
Total Scalar Curvature

scholarly journals Foliation by Area-constrained Willmore Spheres Near a Nondegenerate Critical Point of the Scalar Curvature

2018 ◽  
Vol 2020 (19) ◽  
pp. 6539-6568
Author(s):  
Norihisa Ikoma ◽  
Andrea Malchiodi ◽  
Andrea Mondino
Keyword(s):  
Riemannian Manifold ◽  
Scalar Curvature ◽  
Critical Point ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Multiplicity Result ◽  
Round Sphere ◽  
Willmore Energy ◽  
Nondegenerate Critical Point ◽  
Three Dimensional Space

Abstract Let $(M,g)$ be a three-dimensional Riemannian manifold. The goal of the paper is to show that if $P_{0}\in M$ is a nondegenerate critical point of the scalar curvature, then a neighborhood of $P_{0}$ is foliated by area-constrained Willmore spheres. Such a foliation is unique among foliations by area-constrained Willmore spheres having Willmore energy less than $32\pi $; moreover, it is regular in the sense that a suitable rescaling smoothly converges to a round sphere in the Euclidean three-dimensional space. We also establish generic multiplicity of foliations and the 1st multiplicity result for area-constrained Willmore spheres with prescribed (small) area in a closed Riemannian manifold. The topic has strict links with the Hawking mass.

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