6 citations · 6 across the 2 of their papers we have counts for
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Darboux transforms and spectral curves of constant mean curvature surfaces revisited
Emma Carberry, Katrin Leschke, Franz Pedit
We study the geometric properties of Darboux transforms of constant mean curvature (CMC) surfaces and use these transforms to obtain an algebro-geometric representation of constant…
Sequences of Willmore surfaces
K. Leschke, F. Pedit
In this paper we develop the theory of Willmore sequences for Willmore surfaces in the 4-sphere. We show that under appropriate conditions this sequence has to terminate. In this c…
Willmore tori in the 4-sphere with nontrivial normal bundle
K. Leschke, F. Pedit, U. Pinkall
We characterize Willmore tori in the 4-sphere with nontrivial normal bundle as Twistor projections of elliptic curves in complex projective space or as inverted minimal tori (with…
Envelopes and osculates of Willmore surfaces
K. Leschke, F. Pedit
We view conformal surfaces in the 4--sphere as quaternionic holomorphic curves in quaternionic projective space. By constructing enveloping and osculating curves, we obtain new hol…