Quasi-minimizing surfaces in hyperbolic space.
Diameter bounds for convex surfaces with pinched mean curvature.
Trapping quasiminimizing submanifolds in spaces of negative curvature.
Quasiflats in Hadamard spaces
Flats in Spaces with Convex Geodesic Bicombings
In spaces of nonpositive curvature the existence of isometrically embedded flat (hyper)planes is often granted by apparently weaker conditions on large scales.We show that some such results remain valid for metric spaces with non-unique geodesic segments under suitable convexity assumptions on the distance function along distinguished geodesics. The discussion includes, among other things, the Flat Torus Theorem and Gromov’s hyperbolicity criterion referring to embedded planes. This generalizes...
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