EMBEDDED CONSTANT MEAN CURVATURE TORI IN THE THREE-SPHERE

By Ben Andrews, Haizhong Li. 2012

75 citations recorded by the source corpus.

We prove that any constant mean curvature embedded torus in the three dimensional sphere is axially symmetric, and use this to give a complete classification of such surfaces for any given value of the mean curvature.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/41cbb5e2e277ba587dd2d049a108524a84deadd4

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. S. Brendle
2. Ben Andrews
3. Robert Haslhofer
4. Hong-wei Xu
5. Chao Xia
6. Burkhard Wilking
7. J. Gu
8. A. Malchiodi

In Geometry and Topology

1. S. Brendle
2. Ben Andrews
3. Robert Haslhofer
4. Hong-wei Xu
5. Burkhard Wilking
6. A. Malchiodi
7. Bruce Kleiner
8. J. Gu

Citations in the corpus

• Moduli of continuity, isoperimetric profiles, and multi-point estimates in geometric heat equations (2014, methodology): “A full classification of such tori, accomplished using ODE methods, is also given in [17].”
• Minimal surfaces in $$S^3$$: a survey of recent results (2013, background): “serts that a constant mean curvature surface of genus 1 has no umbilic points, and the norm of the trace-free part of the second fundamental form still satisfies a Simons-type identity. Andrews and Li [4] observed that the proof of Theorem 3.8 can be adapted to show that any embedded constant mean cu”