We formulate several conjectures on mean convex domains in the Euclidean spaces, as well as in more general spaces with lower bonds on their scalar curvatures, and prove a few theorems motivating these conjectures.
Static Manifolds with Boundary and Rigidity of Scalar Curvature and Mean Curvature
Scalar curvature, mean curvature and harmonic maps to the circle
Deformation of the scalar curvature and the mean curvature
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