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October 2022 The behaviour of the mean curvature flow for pinched submanifolds in rank one symmetric spaces
Naoyuki Koike
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Osaka J. Math. 59(4): 905-950 (October 2022).

Abstract

In this paper, we consider the mean curvature flow starting from closed submanifolds in rank one symmetric spaces satisfying some pinching condition for the norm of the second fundamental form. We prove that, under some additional condition, the closed submanifold satisfying the pinching condition collapses to a round point in finite time or converges to a totally geodesic submanifold in infinite time along the mean curvature flow.

Citation

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Naoyuki Koike. "The behaviour of the mean curvature flow for pinched submanifolds in rank one symmetric spaces." Osaka J. Math. 59 (4) 905 - 950, October 2022.

Information

Received: 11 May 2021; Revised: 20 August 2021; Published: October 2022
First available in Project Euclid: 4 October 2022

Subjects:
Primary: 53E10
Secondary: 53C35

Rights: Copyright © 2022 Osaka University and Osaka Metropolitan University, Departments of Mathematics

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Vol.59 • No. 4 • October 2022
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