Minimal Surfaces
Identifieur interne : 000087 ( Main/Exploration ); précédent : 000086; suivant : 000088Minimal Surfaces
Auteurs : Ulrich Dierkes [Allemagne] ; Stefan Hildebrandt [Allemagne] ; Friedrich Sauvigny [Allemagne]Source :
- Grundlehren der mathematischen Wissenschaften [ 0072-7830 ] ; 2010.
Abstract
Abstract: Minimal surfaces are classically defined as surfaces of zero mean curvature in ℝ3. Choosing conformal parameters, one may extend this definition by requiring that a minimal surface X:Ω→ℝ3 is a nonconstant harmonic mapping in conformal representation, and similarly surfaces of prescribed mean curvature are defined. This allows for isolated singular points of X in Ω, so-called branch points, which are discussed in later chapters. If a minimal surface can be represented as graph of a scalar function, one is led to a nonparametric minimal surface satisfying the minimal surface equation. For entire solutions of this equation the celebrated Bernstein theorem is derived as well as a curvature estimate due to E. Heinz which in turn implies Bernstein’s result.
Url:
DOI: 10.1007/978-3-642-11698-8_2
Affiliations:
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Choosing conformal parameters, one may extend this definition by requiring that a minimal surface X:Ω→ℝ3 is a nonconstant harmonic mapping in conformal representation, and similarly surfaces of prescribed mean curvature are defined. This allows for isolated singular points of X in Ω, so-called branch points, which are discussed in later chapters. If a minimal surface can be represented as graph of a scalar function, one is led to a nonparametric minimal surface satisfying the minimal surface equation. For entire solutions of this equation the celebrated Bernstein theorem is derived as well as a curvature estimate due to E. Heinz which in turn implies Bernstein’s result.</div></front></TEI><affiliations><list><country><li>Allemagne</li></country><region><li>District de Cologne</li><li>Rhénanie-du-Nord-Westphalie</li></region><settlement><li>Bonn</li></settlement></list><tree><country name="Allemagne"><noRegion><name sortKey="Dierkes, Ulrich" sort="Dierkes, Ulrich" uniqKey="Dierkes U" first="Ulrich" last="Dierkes">Ulrich Dierkes</name></noRegion><name sortKey="Dierkes, Ulrich" sort="Dierkes, Ulrich" uniqKey="Dierkes U" first="Ulrich" last="Dierkes">Ulrich Dierkes</name><name sortKey="Hildebrandt, Stefan" sort="Hildebrandt, Stefan" uniqKey="Hildebrandt S" first="Stefan" last="Hildebrandt">Stefan Hildebrandt</name><name sortKey="Sauvigny, Friedrich" sort="Sauvigny, Friedrich" uniqKey="Sauvigny F" first="Friedrich" last="Sauvigny">Friedrich Sauvigny</name><name sortKey="Sauvigny, Friedrich" sort="Sauvigny, Friedrich" uniqKey="Sauvigny F" first="Friedrich" last="Sauvigny">Friedrich Sauvigny</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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