REVIEW 1 cited by
Uniqueness of certain cylindrical tangent cones
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
abstract
We show that the cylindrical tangent cone $C\times \mathbf{R}$ for an area-minimizing hypersurface is unique, where $C$ is the Simons cone $C_S= C(S^3\times S^3)$. Previously Simon proved a uniqueness result for cylindrical tangent cones that applies to a large class of cones $C$, however not to the Simons cone. The main new difficulty is that the cylindrical cone $C_S\times \mathbf{R}$ is not integrable, and we need to develop a suitable replacement for Simon's infinite dimensional Lojasiewicz inequality in the setting of tangent cones with non-isolated singularities.
Forward citations
Cited by 1 Pith paper
-
Generic regularity for minimizing hypersurfaces in dimension 11
Area-minimizing hypersurfaces are generically smooth in ambient dimension 11 after a C-infinity-small perturbation of the boundary or metric, and in dimensions 12 and up the singular set has dimension at most n-10-epsilon_n.
Discussion (0). Continue with ORCID to comment.