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arXiv · 2309.04176

Collapsing of Mean Curvature Flow of Hypersurfaces to Complex Submanifolds

Farnaz Ghanbari·Samreena
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Abstract

In this paper, we produce explicit examples of mean curvature flow of (2m-1)-dimensional submanifolds which converge to (2m-2)-dimensional submanifolds at a finite time. These examples are a special class of hyperspheres in $\mathbb{C}^{m}$ with a $U(m)$-invariant K\"ahler metrics. We first discuss the mean curvature flow problem and then investigate the type of singularities for them.

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Farnaz Ghanbari, Samreena. 2023-09-08. Collapsing of Mean Curvature Flow of Hypersurfaces to Complex Submanifolds. https://arxiv.org/abs/2309.04176

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