The Geometry of Minimal Surfaces of Finite Genus I: Curvature Estimates and Quasiperiodicity

By W. H. Meeks, Joaquín Pérez, A. Ros. 2004

56 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/507caafc7846d34d651bca3bb816e1dbd960495b

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In Applied Mathematics

1. W. H. Meeks
2. Joaquín Pérez
3. H. Rosenberg
4. W. Minicozzi
5. T. Colding
6. A. Ros
7. Reto Muller
8. Leili Shahriyari

In Geometry and Topology

1. W. H. Meeks
2. Joaquín Pérez
3. H. Rosenberg
4. W. Minicozzi
5. T. Colding
6. A. Ros
7. Reto Muller
8. J. Lott

Citations in the corpus

• The space of embedded minimal surfaces of fixed genus in a 3-manifold V; Fixed genus (2005, result): “Some of the results of the present paper were announced previously and have already been widely used to study infinite topology minimal surfaces; see, e.g., [MeP], [ MePRs1 ], [MePRs2], [MePRs3], and [P].”
• The space of embedded minimal surfaces of fixed genus in a 3-manifold IV; Locally simply connected (2002, unknown): “This is an area of much current research, see [CM6], the work of Meeks, J. Perez and A. Ros, [ MePRs1 ], [MePRs2], and [MePRs3], and references therein.”
• The uniqueness of the helicoid (2005, background): “[23] W. H. Meeks III and H. Rosenberg, The geometry and conformal structure of properly embedded minimal surfaces of finite topology in R3, Invent.”
• The classical theory of minimal surfaces (2011, methodology): “Meeks, Pérez and Ros (Theorem 5 in [125]) have combined the last statement with deeper arguments using the results of Colding and Minicozzi, which let us exchange the finite topology assumption by the weaker hypothesis of finite genus.”
• Conformal properties in classical minimal surface theory (2004, methodology): “Theorem 34. [ 74 ] If M ⊂ R3 is a connected complete embedded minimal surface in R3 with finite genus and locally bounded Gaussian curvature, then M is”
• The theory of minimal surfaces in M × R (2005, unknown): “In 850 W. H. Meeks, III and H. Rosenberg CMH R2 × R we consider the homothetically scaled and translated surfaces ̃(n) = 1 fn(p(n)) ( (n) − p(n)).”