Energy quantization for Willmore surfaces with bounded index

Dorian Martino

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arXiv · 2305.08668

Energy quantization for Willmore surfaces with bounded index

Dorian Martino

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Abstract

We prove an energy quantization result for Willmore surfaces with bounded index, whether the underlying Riemann surfaces degenerates in the moduli space or not. To do so, we translate the question on the conformal Gauss map's point of view. In particular, we prove that in a neck or a collar region, the conformal Gauss map converges to a light-like geodesic in the De Sitter space.

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Dorian Martino. 2023-05-15. Energy quantization for Willmore surfaces with bounded index. https://arxiv.org/abs/2305.08668

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