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<p>We show that the product of two round shrinking spheres is an isolated self-shrinker in any codimension, modulo rotations. Moreover we prove explicit Łojasiewicz inequalities near such products. Łojasiewicz inequalities were previously used by Schulze to prove uniqueness of tangent mean curvature flows at compact shrinkers; our results provide an explicit rate of convergence to products of two spheres.</p>

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Rigidity and Łojasiewicz inequalities for Clifford self-shrinkers

  • 期刊论文

  • 发表日期：

    2025年5月27日

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  • Ao Sun,
  • Jonathan J. Zhu

摘要

We show that the product of two round shrinking spheres is an isolated self-shrinker in any codimension, modulo rotations. Moreover we prove explicit Łojasiewicz inequalities near such products. Łojasiewicz inequalities were previously used by Schulze to prove uniqueness of tangent mean curvature flows at compact shrinkers; our results provide an explicit rate of convergence to products of two spheres.