Theoretical analysis proves uniqueness of cylindrical Simons tangent cones in area-minimizing hypersurfaces, establishing new analytical techniques for non-isolated singularities.
We show that the cylindrical tangent cone C× R C × R for an area-minimizing hypersurface is unique, where C C is the Simons cone CS= C(S³× S³) C S = C ( S 3 × S 3 ) . Previously Simon proved a uniqueness result for cylindrical tangent cones that applies to a large class of cones C C , however not to the Simons cone. The main new difficulty is that the cylindrical cone CS× R C S × R is not integrable, and we need to develop a suitable replacement for Simon’s infinite dimensional Łojasiewicz inequality in the setting of tangent cones with non-isolated singularities.
No takes yet. Share an insight, caveat, or question.
Gábor Székelyhidi (2026) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: