This work demonstrates energy quantization and strong compactness in constrained willmore surfaces, highlighting implications for mean curvature.
We establish an energy quantization for constrained Willmore surfaces, where the constraints are given by area, volume, and total mean curvature, assuming that the underlying conformal structures remain bounded. Furthermore, we show strong compactness of constrained Willmore surfaces under some energy threshold, proving in particular the strong compactness of minimizers of two previously studied problems.
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Scharrer et al. (2025) studied this question.
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