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arXiv · 2509.24426

Finite number of traces for Mumford-Shah minimizers in dimension 2

Camille Labourie·Antoine Lemenant
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Abstract

In this short note, we answer a question raised by E. De Giorgi, showing that a Mumford-Shah minimizer in dimension 2 can only admit three maximum limit values as approaching the singular set. This result stems from tools developed in the early 2000's by G. David, A. Bonnet, and J.-C. L\'eger.

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Camille Labourie, Antoine Lemenant. 2025-09-29. Finite number of traces for Mumford-Shah minimizers in dimension 2. https://arxiv.org/abs/2509.24426

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