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math.DG2024
3-circle Theorem for Willmore surfaces II--degeneration of the complex structure
Yuxiang Li, Hao Yin, Jie Zhou
We study the compactness of Willmore surfaces without assuming the convergence of the induced complex structures. In particular, we compute the energy loss in the neck in terms of…
math.DG2024
3-circle Theorem for Willmore surface I
Yuxiang Li, Hao Yin
In this paper, we study the blow-up of Willmore surfaces. By using the 3-circle theorem, we prove a decay estimate of the second fundamental form along the neck region. This estima…