The structure of complete embedded surfaces with constant mean curvature

Korevaar, Nicholas J.; Kusner, Rob; Solomon, Bruce

doi:10.4310/jdg/1214443598

Cited by 222 publications

(227 citation statements)

References 11 publications

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“…Before stating Theorem 2.2, we describe the notion of the flux of a 1-cycle in an H-surface; see for instance [14,15,31] for further discussion of this invariant.…”

Section: An Extrinsic Curvature Estimate For Certain Planar Domainsmentioning

confidence: 99%

On curvature estimates for constant mean curvature surfaces

Tinaglia¹

2012

Geometric Analysis

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“…Before stating Theorem 2.2, we describe the notion of the flux of a 1-cycle in an H-surface; see for instance [14,15,31] for further discussion of this invariant.…”

Section: An Extrinsic Curvature Estimate For Certain Planar Domainsmentioning

confidence: 99%

On curvature estimates for constant mean curvature surfaces

Tinaglia¹

2012

Geometric Analysis

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“…This equation known as the "balancing formula" or "flux formula" is due to R. Kusner (see [9]; also in [10,8]). It is a conservation law in the sense of Noether that reflects the fact that the area (the potential) is invariant under the group of translations of Euclidean space.…”

Section: Mean Curvature Graphs and The Laplacianmentioning

confidence: 99%

A New Proof of a Characterization of Small Spherical Caps

López

2009

Results. Math.

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It is known that planar disks and small spherical caps are the only constant mean curvature graphs whose boundary is a round circle. Usually, the proof invokes the Maximum Principle for elliptic equations. This paper presents a new proof of this result motivated by an article due to Reilly. Our proof utilizes a flux formula for surfaces with constant mean curvature together with integral equalities on the surface.

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“…Since Delaunay surfaces are ubiquitous in the study of CMC surfaces with embedded ends [9], we feel the necessity to give a self-contained account of Delaunay surfaces in the DPW framework. Here we thus describe the construction of the associated family of Delaunay surfaces using holomorphic data on the twice-punctured Riemann sphere.…”

Section: Introductionmentioning

confidence: 99%