A Liouville‐type theorem for cylindrical cones
Copyright policy )A Liouville‐type theorem for cylindrical cones
AbstractSuppose that is a smooth strictly minimizing and strictly stable minimal hypercone (such as the Simons cone), , and a complete embedded minimal hypersurface of lying to one side of . If the density at infinity of is less than twice the density of , then we show that , where is the Hardt–Simon foliation of . This extends a result of L. Simon, where an additional smallness assumption is required for the normal vector of .
- Northwestern University United States
- University of Notre Dame United States
Differential geometry of immersions (minimal, prescribed curvature, tight, etc.), Mathematics - Differential Geometry, Applications of PDEs on manifolds, Global submanifolds, Rigidity results, Mathematics - Analysis of PDEs, Differential Geometry (math.DG), Foliations (differential geometric aspects), minimal hypersurfaces, cylindrical hypercones, FOS: Mathematics, Liouville theorem, Analysis of PDEs (math.AP)
Differential geometry of immersions (minimal, prescribed curvature, tight, etc.), Mathematics - Differential Geometry, Applications of PDEs on manifolds, Global submanifolds, Rigidity results, Mathematics - Analysis of PDEs, Differential Geometry (math.DG), Foliations (differential geometric aspects), minimal hypersurfaces, cylindrical hypercones, FOS: Mathematics, Liouville theorem, Analysis of PDEs (math.AP)
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