论文标题
某些圆柱形切线锥的独特性
Uniqueness of certain cylindrical tangent cones
论文作者
论文摘要
我们表明，用于区域最小化的超曲面的圆柱形切线锥$ C \ times \ times \ Mathbf {r} $是唯一的，其中$ c $是Simons Cone $ C_S = C（S^3 \ times s^3）$。以前，西蒙证明了适用于大型锥体$ c $的圆柱形切线锥的独特结果，但不适用于西蒙斯锥体。主要的新难度是圆柱锥$ C_S \ times \ Mathbf {r} $是不可集成的，我们需要在具有非相差奇异性的切线锥体中为Simon的无限尺寸Lojasiewicz不平等开发合适的替换。
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.
