Search results for "minimal lamination"

showing 2 items of 2 documents

Extending an example by Colding and Minicozzi

2018

Extending an example by Colding and Minicozzi, we construct a sequence of properly embedded minimal disks $\Sigma_i$ in an infinite Euclidean cylinder around the $x_3$-axis with curvature blow-up at a single point. The sequence converges to a non smooth and non proper minimal lamination in the cylinder. Moreover, we show that the disks $\Sigma_i$ are not properly embedded in a sequence of open subsets of $\mathbb{ R}^3$ that exhausts $\mathbb{ R}^3$.

Mathematics - Differential GeometryvariaatiolaskentaLamination (topology)Curvatureminimal surfaces01 natural sciencesCombinatoricsdifferentiaaligeometria510 Mathematics0103 physical sciencesEuclidean geometryFOS: MathematicsCylinderPhysics::Atomic Physics0101 mathematicsMathematicsSequence010102 general mathematicsSigmaminimal laminationsColding-Minicozzi theoryDifferential geometryDifferential Geometry (math.DG)53A10 (Primary)010307 mathematical physicsGeometry and TopologyMathematics::Differential GeometrySingle point
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On the topology of surfaces with the generalised simple lift property.

2020

In this paper, we study the geometry of surfaces with the generalised simple lift property. This work generalises previous results by Bernstein and Tinaglia, and it is motivated by the fact that leaves of a minimal lamination obtained as a limit of a sequence of properly embedded minimal disks satisfy the generalised simple lift property.

Pure mathematicsHyperbolic geometryminimal laminationAlgebraic geometryminimal surfaces01 natural sciencesLift (mathematics)differentiaaligeometriaMathematics - Geometric Topology510 Mathematics0103 physical sciencesFOS: MathematicsLimit of a sequence53A10 51H050101 mathematicstopologiaSimple lift propertyMathematicsProjective geometryColding and minicozzi theoryOriginal PaperMinimal surface010102 general mathematicscolding and minicozzi theory53A10Geometric Topology (math.GT)Minimal surfacesMinimal lamination16. Peace & justiceDifferential geometry51H05010307 mathematical physicsGeometry and Topologygeometriasimple lift propertyGeometriae dedicata
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