Search results for " 53A10"

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On the shape of compact hypersurfaces with almost constant mean curvature

2015

The distance of an almost constant mean curvature boundary from a finite family of disjoint tangent balls with equal radii is quantitatively controlled in terms of the oscillation of the scalar mean curvature. This result allows one to quantitatively describe the geometry of volume-constrained stationary sets in capillarity problems.

Mathematics - Differential GeometryMean curvatureOscillationApplied MathematicsGeneral Mathematics010102 general mathematicsMathematical analysisScalar (mathematics)Boundary (topology)TangentMetric Geometry (math.MG)Disjoint sets01 natural sciences010101 applied mathematicsMathematics - Analysis of PDEsMean curvature capillarity theory quantitative estimates Alexandrov theorem.Differential Geometry (math.DG)Mathematics - Metric Geometry49Q10 49Q20 53A10FOS: MathematicsMathematics::Differential Geometry0101 mathematicsConstant (mathematics)Analysis of PDEs (math.AP)Mathematics
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The method of moving planes: a quantitative approach

2018

We review classical results where the method of the moving planes has been used to prove symmetry properties for overdetermined PDE's boundary value problems (such as Serrin's overdetermined problem) and for rigidity problems in geometric analysis (like Alexandrov soap bubble Theorem), and we give an overview of some recent results related to quantitative studies of the method of moving planes, where quantitative approximate symmetry results are obtained.

Mathematics - Differential Geometryoverdetermined problem010102 general mathematicsmean curvaturelcsh:QA299.6-43335N25; 35B35; 53A10; 53C24; 35B50; 35B51; 35J70alexandrov soap bubble theoremlcsh:Analysisstability01 natural sciencesAlexandrov Soap Bubble Theorem; overdetermined problems; rigidity; stability; mean curvature; moving planesMathematics - Analysis of PDEsrigidityDifferential Geometry (math.DG)Settore MAT/05 - Analisi Matematicaoverdetermined problemsFOS: Mathematics0101 mathematicsmoving planesAnalysis of PDEs (math.AP)
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