Search results for "Quantitative estimates"

showing 2 items of 2 documents

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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Sharp dimension free quantitative estimates for the Gaussian isoperimetric inequality

2017

We provide a full quantitative version of the Gaussian isoperimetric inequality: the difference between the Gaussian perimeter of a given set and a half-space with the same mass controls the gap between the norms of the corresponding barycenters. In particular, it controls the Gaussian measure of the symmetric difference between the set and the half-space oriented so to have the barycenter in the same direction of the set. Our estimate is independent of the dimension, sharp on the decay rate with respect to the gap and with optimal dependence on the mass.

Statistics and ProbabilityGaussianGaussian isoperimetric inequality01 natural sciencesPerimeterSet (abstract data type)symbols.namesakeMathematics - Analysis of PDEsDimension (vector space)quantitative isoperimetric inequalityFOS: MathematicsMathematics::Metric Geometry0101 mathematicsSymmetric differenceGaussian isoperimetric inequalityQuantitative estimatesMathematics010102 general mathematicsMathematical analysisProbability (math.PR)49Q20Gaussian measure010101 applied mathematicssymbolsHigh Energy Physics::Experiment60E15Statistics Probability and UncertaintyMathematics - ProbabilityAnalysis of PDEs (math.AP)
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