Search results for "Plateau's problem"

showing 3 items of 3 documents

On the plateau problem for surfaces of constant mean curvature

1970

Mean curvature flowMean curvatureApplied MathematicsGeneral MathematicsGeometryCenter of curvatureRadius of curvaturePlateau's problemMathematicsCommunications on Pure and Applied Mathematics
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The Plateau-Bézier Problem

2003

We study the Plateau problem restricted to polynomial surfaces using techniques coming from the theory of Computer Aided Geometric Design. The results can be used to obtain polynomial approximations to minimal surfaces. The relationship between harmonic Bezier surfaces and minimal surfaces with free boundaries is shown.

PolynomialGeometric designMinimal surfaceMathematical analysisConstant-mean-curvature surfaceGeometryBézier curvePlateau (mathematics)Plateau's problemBernstein polynomialMathematics
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2021

Abstract We extend the classical Carathéodory extension theorem to quasiconformal Jordan domains (Y, dY ). We say that a metric space (Y, dY ) is a quasiconformal Jordan domain if the completion ̄Y of (Y, dY ) has finite Hausdorff 2-measure, the boundary ∂Y = ̄Y \ Y is homeomorphic to 𝕊1, and there exists a homeomorphism ϕ: 𝔻 →(Y, dY ) that is quasiconformal in the geometric sense. We show that ϕ has a continuous, monotone, and surjective extension Φ: 𝔻 ̄ → Y ̄. This result is best possible in this generality. In addition, we find a necessary and sufficient condition for Φ to be a quasiconformal homeomorphism. We provide sufficient conditions for the restriction of Φ to 𝕊1 being a quasi…

Surjective functionCombinatoricsMetric spaceApplied MathematicsDomain (ring theory)Hausdorff spaceBoundary (topology)Geometry and TopologyQuasicirclePlateau's problemAnalysisHomeomorphismMathematicsAnalysis and Geometry in Metric Spaces
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