scholarly journals On the volume functional of compact manifolds with boundary with constant scalar curvature

2009 ◽  
Vol 36 (2) ◽  
pp. 141-171 ◽  
Author(s):  
Pengzi Miao ◽  
Luen-Fai Tam
Keyword(s):  
Scalar Curvature ◽  
Constant Scalar Curvature ◽  
Compact Manifolds ◽  
Manifolds With Boundary ◽  
Volume Functional

Compact manifolds of constant scalar curvature

1991 ◽  
Vol 40 (1) ◽  
Author(s):  
Sharief Deshmukh ◽  
M.A. Al-Gwaiz
Keyword(s):  
Scalar Curvature ◽  
Constant Scalar Curvature ◽  
Compact Manifolds

4-Dimensional manifolds with nonnegative scalar curvature and CMC boundary

2020 ◽  
pp. 1950094
Author(s):  
Yaohua Wang
Keyword(s):  
Scalar Curvature ◽  
Upper Bound ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Outer Boundary ◽  
Compact Manifolds ◽  
Manifolds With Boundary ◽  
Flat Extension ◽  
Asymptotically Flat ◽  
3 Dimensional

In this paper, we will consider 4-dimensional manifolds with nonnegative scalar curvature and constant mean curvature (CMC) boundary. For compact manifolds with boundary, the influence of the nonnegativity of the region scalar curvature to the geometry of the boundary is considered. Some inequalities are established for manifolds with inner boundary and outer boundary. Even for compact manifolds without inner boundary, we can obtain some inequalities involving the geometric quantities of the boundary and give some obstruction. We also discuss the 4-dimensional asymptotically flat extension of the 3-dimensional Bartnik data with CMC boundary and provide the upper bound of the Bartnik mass.

scholarly journals Compactness and non-compactness for the Yamabe problem on manifolds with boundary

2017 ◽  
Vol 2017 (724) ◽  
Author(s):  
Marcelo M. Disconzi ◽  
Marcus A. Khuri
Keyword(s):  
Scalar Curvature ◽  
Mean Curvature ◽  
Constant Scalar Curvature ◽  
Yamabe Problem ◽  
Riemannian Structure ◽  
Manifolds With Boundary ◽  
Conformal Deformation ◽  
Zero Mean Curvature

AbstractWe study the problem of conformal deformation of Riemannian structure to constant scalar curvature with zero mean curvature on the boundary. We prove compactness for the full set of solutions when the boundary is umbilic and the dimension

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