Closed surfaces with minimal total absolute curvature in Cartan-Hadamard 3-manifolds bound flat convex bodies.
Schneider,Convex bodies: the Brunn-Minkowski theory, expanded, Encyclopedia of Mathematics and its Applications, vol
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Total absolute curvature and rigidity of surfaces in Cartan-Hadamard manifolds
Closed surfaces with minimal total absolute curvature in Cartan-Hadamard 3-manifolds bound flat convex bodies.