Minimal surfaces in the three-sphere by doubling the Clifford torus
By N. Kapouleas, Seong-Deog Yang. 2010
71 citations recorded by the source corpus.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/9cdf770907cac7fe6d24f24c62e27cb452c18329
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In Applied Mathematics
In Geometry and Topology
Citations in the corpus
- Stable solutions of the Allen–Cahn equation in dimension 8 and minimal cones (2011, background): “This list of examples does not exhaust the list of all minimal hypersurfaces in S and further examples of minimal hypersurfaces in S can be found for example in [30], [35] or in [29].”
- Complete Embedded Self-Translating Surfaces Under Mean Curvature Flow (2010, background): “6 was corrected by Kapouleas (see [10] page 281) and should be replaced by the one given here.”
- Embedded minimal tori in S3 and the Lawson conjecture (2012, background): “The resulting surfaces have small mean curvature, and Kapouleas and Yang employed the implicit function theorem to deform these surfaces to exact solutions of the minimal surface equation.”
- Comparing the Morse index and the first Betti number of minimal hypersurfaces (2016, background): “For instance, the construction by Kapouleas-Yang [17] yields sequences of minimal surfaces with uniformly bounded area and unbounded genus.”
- Free boundary minimal surfaces in the unit ball : recent advances and open questions (2019, background): “In the past decade, we have witnessed tremendous success of gluing techniques in a wide range of geometric variational problems, including for example closed minimal surfaces in S [57] [52] [56], complete constant mean curvature surfaces in R(3) [4], Special Lagrangian cones [36] [37] [38] and self ”
- Minimal surfaces in $$S^3$$: a survey of recent results (2013, methodology): “mean curvature, the mean curvature of the surface Σm,ζ is small when m is sufficiently large (see [30], Lemma 3.”
- Free boundary minimal surfaces in the unit three-ball via desingularization of the critical catenoid and the equatorial disc (2017, methodology): “minimal surfaces in S3(1) have been obtained by Lawson’s method [4] and by singular perturbation methods [35], [33], [55] and [34].”