Energy quantization for constrained Willmore surfaces

2025/05/26 by Christian Scharrer, Scharrer, Christian, Alexander West +1
Mathematics · Physics and Astronomy · #49Q10 #53A30 #53C42 #Advanced Differential Geometry Research #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2505.19898

openalex publication_date 2025/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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