Peer-reviewedCC BYInventiones mathematicae
Uniqueness of certain cylindrical tangent cones
Abstract
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.
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BibTeX
@article{szekelyhidi2026uniqueness,
title = {{Uniqueness of certain cylindrical tangent cones}},
author = {Gábor Székelyhidi},
journal = {Inventiones mathematicae},
year = {2026},
month = aug,
doi = {10.1007/s00222-026-01445-1},
url = {https://doi.org/10.1007/s00222-026-01445-1},
note = {CC BY},
}
RIS
TY - JOUR
TI - Uniqueness of certain cylindrical tangent cones
AU - Gábor Székelyhidi
PY - 2026
DA - 2026/08/21
JO - Inventiones mathematicae
DO - 10.1007/s00222-026-01445-1
UR - https://doi.org/10.1007/s00222-026-01445-1
AB - 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 C_S= C(S^3× S^3) 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 C_S× 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.
SN - 0020-9910
SN - 1432-1297
ER -