Proper minimal immersions with sublinear height growth must have Euclidean volume growth, implying an optimal Bernstein theorem for stable hypersurfaces.
P\'erez, Minimal surfaces of finite genus: Classification, dynamics and laminations , ICM Proceedings 2026, to appear
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The distance between minimal hypersurfaces is a viscosity supersolution to an elliptic PDE, with extensions to parabolic PDEs when evolving by mean curvature flow.
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Minimal submanifolds confined in space
Proper minimal immersions with sublinear height growth must have Euclidean volume growth, implying an optimal Bernstein theorem for stable hypersurfaces.
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Distance between minimal surfaces and flows
The distance between minimal hypersurfaces is a viscosity supersolution to an elliptic PDE, with extensions to parabolic PDEs when evolving by mean curvature flow.