Closed surfaces with minimal total absolute curvature in Cartan-Hadamard 3-manifolds bound flat convex bodies.
Gromov,Lectures on immersions with controlled curvatures, arXiv:2511.01796 (2025).https: //arxiv.org/abs/2511.01796.↑11
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A lower bound on average normal curvature for closed submanifolds in Riemannian domains is given via an n-trace convexity invariant, extending Petrunin's result to Cartan-Hadamard geodesic balls and similar settings.
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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.
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Normal curvature bounds for immersions into Riemannian domains
A lower bound on average normal curvature for closed submanifolds in Riemannian domains is given via an n-trace convexity invariant, extending Petrunin's result to Cartan-Hadamard geodesic balls and similar settings.