For each integer \(k \ge 2\) we apply PDE gluing methods to desingularize certain collections of intersecting Clifford tori, thus producing sequences of minimal surfaces embedded in the round three-sphere. The collections of the Clifford tori we use consist of either k Clifford tori intersecting with maximal symmetry along two orthogonal great circles (lying on orthogonally complementary two-planes) or 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. The former two circles get desingularized by using singly periodic Karcher–Scherk towers of order k as models, so that after rescaling the sequences of minimal surfaces converge smoothly on compact subsets to the Karcher–Scherk tower of order k. Near the other 2k circles (in the latter case) the corresponding rescaled sequences converge to a singly periodic Scherk surface. The simpler examples of the first type, where the number of handles desingularizing each circle is the same, resemble surfaces constructed by Choe and Soret (Math Ann 364(3–4):763–776, 2016) by different methods. There are many new examples which are more complicated and on which the numbers of handles for the two circles differ. All examples of the latter type are new as well.

对于每个整数\（k \ ge 2 \），我们应用PDE胶合方法将相交的Clifford花托的某些集合解单数化，从而生成嵌入在圆形三球体中的最小曲面的序列。我们使用的Clifford花托的集合包括沿着两个正交大圆（位于正交互补的两个平面上）以最大对称性相交的k个Clifford花托或相同的k Clifford花托，并辅之以与原始两个等距距离相等的Clifford花托。相交圆，使后一个圆环与前一个k正交沿一对不相交的正交圆的圆环。前两个圆通过使用阶数为k的单周期Karcher-Scherk塔作为模型而被分解为异形，因此，在重新缩放最小曲面的序列后，其紧致子集平滑地收敛到k阶的Karcher-Scherk塔。接近其他2 k圈（在后一种情况下）对应的重新缩放的序列会聚到单个周期性的Scherk表面。第一种类型的简单示例（每个圆的去奇点化处理的手柄数相同）类似于通过不同方法由Choe和Soret构造的曲面（Math Ann 364（3-4）：763-776，2016）。有许多新示例更加复杂，两个圆圈上的手柄数量也有所不同。后一种类型的所有示例也是新的。