Estimates for parametric elliptic integrands

By T. Colding, W. Minicozzi. 2002

88 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/798bb8c8d676121ed25670cb403dcdfd98b9bb55

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. W. H. Meeks
2. Joaquín Pérez
3. W. Minicozzi
4. T. Colding
5. A. Ros
6. Camillo De Lellis
7. H. Rosenberg
8. J. Spruck

In Computational Theory and Mathematics

1. T. Colding
2. W. Minicozzi
3. W. H. Meeks
4. Camillo De Lellis
5. J. Spruck
6. Ling Xiao
7. Joaquín Pérez
8. A. Ros

In Geometry and Topology

1. W. H. Meeks
2. Joaquín Pérez
3. W. Minicozzi
4. T. Colding
5. A. Ros
6. Camillo De Lellis
7. J. Spruck
8. Ling Xiao

Citations in the corpus

• Conformal properties in classical minimal surface theory (2004, background): “2 in [22]) gave the following useful upper estimate for Area(D) by assuming stability.”
• Minimal submanifolds (2005, unknown): “[15] If Σ ⊂ R(3) is an immersed stable minimal surface with trivial normal bundle and Br0 ⊂ Σ \ ∂Σ, then (8.”
• The space of embedded minimal surfaces of fixed genus in a 3-manifold V; Fixed genus (2005, background): “Th is quadratic area estimate formally follows from the argument in [ CM2 ], but we need the results of the previous subsection to deal with technical difficulties that arise from the lack of regularity of the level sets of the distance function.”
• Complete translating solitons to the mean curvature flow in ℝ3 with nonnegative mean curvature (2020, methodology): “We now follow the Colding-Minicozzi method [9, 10] with appropriate modification, to prove intrinsic area bounds and then curvature bounds.”
• The min--max construction of minimal surfaces (2003, methodology): “In many of the proofs we will use Schoen’s curvature estimate (see [Sc] or [ CM2 ]) for stable minimal surfaces.”
• Stable constant mean curvature surfaces (2008, background): “It follows that the second fundamental form of the leaves of L is continuous on L and L is of class C1,1 (see the related Proposition B.1 in Colding-Minicozzi [10] and see Solomon [56] for a proof of the C1,1-regularity in the minimal foliation case for a three-manifold, without appealing to our ass”
• The Calabi-Yau conjectures for embedded surfaces (2004, methodology): “In this subsection, we recall from [ CM2 ] and [CM4] several important properties of embedded minimal surfaces with bounded curvature.”
• The space of embedded minimal surfaces of fixed genus in a 3-manifold IV; Locally simply connected (2002, background): “Note that by the curvature estimate for stable surfaces, [Sc], [ CM2 ], when Σ is stable then the conclusion of Proposition I.0.11 is that no such surface exists for C1, C2 sufficiently large.”