Duality between cuspidal butterflies and cuspidal S_1^- singularities on maximal surfaces


Abstract


We give criteria for cuspidal butterflies and cuspidal S_1^- (cS_1^-) singularities in terms of the Weierstrass data for maximal surfaces, and also show non-existence of cuspidal S_1^+ (cS_1^+) singularities on maximal surfaces. Moreover, we show duality between these singularities considering the conjugate maximal surfaces each other.

DOI Code: 10.1285/i15900932v38n1p115

Keywords: maximal surface; frontal; cuspidal butterfly; cuspidal $S_k$ singularity

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