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arXiv · 2610.20054

A semi-discrete scheme for horizontal mean curvature flow in the Heisenberg group

A. Cesaroni·M. Novaga·P. Pozzi
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Abstract

The horizontal mean curvature flow is a geometric evolution associated with the horizontal perimeter in sub-Riemannian spaces. In this paper, we introduce a minimizing movement scheme for this flow in the first Heisenberg group $\mathbb{H}$, and prove the existence of a flat flow which is locally $1/2$-Hölder continuous in time, with respect to the $L^1$-distance. The construction applies to arbitrary bounded sets of finite horizontal perimeter and does not require smoothness or symmetry of the initial datum.

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A. Cesaroni, M. Novaga, P. Pozzi. 2026-10-14. A semi-discrete scheme for horizontal mean curvature flow in the Heisenberg group. https://arxiv.org/abs/2610.20054

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