Existence of index-one minimal hypersurfaces with unbounded volume in enlargeable manifolds (dims 3-7) plus 3D scalar curvature rigidity under area-nonincreasing maps.
Examples of stable embedded minimal spheres without area bounds
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
The author proves that there is an open non empty set of metrics on any 3-manifold such that there exists a family of stably embedded minimal 2-spheres whose area is unbounded. This generalizes the work of T. Colding and W. Minicozzi who have shown an analogous result for the torus and B. Dean who showed the positive genus case.
fields
math.DG 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
citing papers explorer
-
Closed minimal surfaces of index one in Riemannian manifolds
Existence of index-one minimal hypersurfaces with unbounded volume in enlargeable manifolds (dims 3-7) plus 3D scalar curvature rigidity under area-nonincreasing maps.