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arXiv · 2012.02065

Uniqueness of certain cylindrical tangent cones

Gábor Székelyhidi
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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.

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Gábor Székelyhidi. 2020-12-03. Uniqueness of certain cylindrical tangent cones. https://arxiv.org/abs/2012.02065

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