Research profile

Marco Radeschi

Works on ancient solutions and mean curvature flow.

NP-RC-9785070000-0001-6167-7136

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  1. Xiaobo Liu

    1 joint worklatest 2020

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2020

math.DGWider flowsv2arXiv:2006.03945

Polar foliations on symmetric spaces and the mean curvature flow

Xiaobo Liu, Marco Radeschi

In this paper, we study polar foliations on simply connected symmetric spaces with non-negative curvature. We will prove that all such foliations are isoparametric as defined by Heintze, Liu and Olmos. We will also prove a splitting theorem which reduces the study of such foliations to polar foliations in compact simply connected symmetric spaces. Moreover, we will show that solutions to mean curvature flow of regular leaves in such foliations are always ancient solutions. This generalizes part of the results of Liu and Terng for the mean curvature flow of isoparametric submanifolds in spheres.

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