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arXiv · 2607.03930

De Giorgi varifold solutions to Mean Curvature Flow: a minimizing movements approach

Tim Laux·Andrea Poiatti
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Abstract

We propose an alternative existence proof of global weak solutions to mean curvature flow and volume preserving mean curvature flow. We prove for the first time for a minimizing movements scheme the unconditional convergence towards a varifold solution, here a De Giorgi solution. The argument is purely variational and does not rely on comparison principles. The key novelty is an alternative proxy for the completely degenerate $L^2$ distance that is more robust than the one of Almgren-Taylor-Wang and Luckhaus-Sturzenhecker.

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Tim Laux, Andrea Poiatti. 2026-07-04. De Giorgi varifold solutions to Mean Curvature Flow: a minimizing movements approach. https://arxiv.org/abs/2607.03930

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