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arXiv · 2510.26458

Monotone Sobolev extensions in metric surfaces and applications to uniformization

Damaris Meier·Noa Vikman·Stefan Wenger
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Abstract

We prove a monotone Sobolev extension theorem for maps to Jordan domains with rectifiable boundary in metric surfaces of locally finite Hausdorff 2-measure. This is then used to prove a uniformization result for compact metric surfaces by minimizing energy in the class of monotone Sobolev maps.

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Damaris Meier, Noa Vikman, Stefan Wenger. 2025-10-30. Monotone Sobolev extensions in metric surfaces and applications to uniformization. https://arxiv.org/abs/2510.26458

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