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• W3154690435 abstract "For each integer $k geq 2$, we apply gluing methods to construct sequences of minimal surfaces embedded in the round $3$-sphere. We produce two types of sequences, all desingularizing collections of intersecting Clifford tori. Sequences of the first type converge to a collection of $k$ Clifford tori intersecting with maximal symmetry along these two circles. Near each of the circles, after rescaling, the sequences converge smoothly on compact subsets to a Karcher-Scherk tower of order $k$. Sequences of the second type desingularize a collection of the same $k$ Clifford tori supplemented by an additional Clifford torus equidistant from the original two circles of intersection, so that the latter torus orthogonally intersects each of the former $k$ tori along a pair of disjoint orthogonal circles, near which the corresponding rescaled sequences converge to a singly periodic Scherk surface. The simpler examples of the first type resemble surfaces constructed by Choe and Soret cite{CS} by different methods where the number of handles desingularizing each circle is the same. There is a plethora of new examples which are more complicated and on which the number of handles for the two circles differs. Examples of the second type are new as well." @default.
• W3154690435 created "2021-04-26" @default.
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• W3154690435 date "2021-04-11" @default.
• W3154690435 modified "2023-10-13" @default.
• W3154690435 title "Minimal surfaces in the three-sphere by desingularizing intersecting Clifford tori" @default.
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• W3154690435 doi "https://doi.org/10.1007/s00208-021-02169-8" @default.
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