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We investigate conditions under which a blowup, i.e. a rescaling in theparameter domain and in the ambient space, of a sequence of constant meancurvature torus immersions into the Euclidean 3-space produces a sequence ofwhich a subsequence converges to a non-trivial minimal surface immersion.

Blowing up sequences of constant mean curvature tori with fixed spectral genus in the Euclidean 3-space to minimal surfaces