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Theorem demonstrates that shrinkers intersect in large balls, indicating connectivity in geometric analysis.
We prove a strong Frankel theorem for mean curvature flow shrinkers in all dimensions: Any two shrinkers in a sufficiently large ball must intersect. In particular, the shrinker itself must be connected in all large balls. The key to the proof is a strong Bernstein theorem for incomplete stable Gaussian surfaces.
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Colding et al. (2025) studied this question.
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