Work

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

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.20054

Authors: Cesaroni, A., Novaga, M., Pozzi, P.

Institutions: University of Padua, University of Pisa, University of Duisburg-Essen

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7222229847

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