47 citations · 277 across the 44 of their papers we have counts for
5 papers · 2 filters
A dichotomy for minimal submanifolds
Tobias Holck Colding, William P. Minicozzi
We survey a circle of recent results showing that a minimal submanifold obeys a dichotomy: either it fills up space, spreading out like a space-filling curve, or it is confined, an…
Liouville theorem for immersed minimal surfaces in any codimension
Tobias Holck Colding, William P. Minicozzi
For a proper immersed minimal disk in with quadratic area growth, we show that any harmonic function whose negative part grows at a slow sub-linear rate is constant. Thi…
Minimal submanifolds confined in space
Tobias Holck Colding, William P. Minicozzi
Already in , there are many minimal hypersurfaces, yet few structural results. We show that minimal submanifolds, of any dimension and codimension, that are confined in s…
Distance between minimal surfaces and flows
Tobias Holck Colding, William P. Minicozzi
We will show that the distance between two minimal hypersurfaces is a Lipschitz continuous supersolution, in the viscosity sense, of a natural elliptic partial differential equatio…
Minimal surfaces with rapid area growth
Tobias Holck Colding, Francisco Martín, William P. Minicozzi
We give examples of proper minimal immersions in Euclidean space with very rapid area growth. The first is a proper embedding into that yields a stable minimal surface,…