An isoperimetric deficit upper bound of the convex domain in a surface of constant curvature

DOI10.1007/s11425-010-4018-3zbMath1209.52004OpenAlexW2004360985MaRDI QIDQ625811

Ming Li, Jia-zu Zhou

Publication date: 25 February 2011

Published in: Science China. Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11425-010-4018-3

zbMATH Keywords

convex setisoperimetric deficitkinematic formulathe surface of constant curvature

Mathematics Subject Classification ID

Integral geometry (53C65) Spherical and hyperbolic convexity (52A55) Convex sets in (2) dimensions (including convex curves) (52A10) Random convex sets and integral geometry (aspects of convex geometry) (52A22)

Related Items (11)

Kinematic formulas of total mean curvatures for hypersurfaces ⋮ Translative containment measure and symmetric mixed isohomothetic inequalities ⋮ Bonnesen-style symmetric mixed inequalities ⋮ Reverse Bonnesen-style inequalities on surfaces of constant curvature ⋮ Reverse Bonnesen style inequalities in a surface \(\mathbb{X}_\epsilon ^2\) of constant curvature ⋮ On Bonnesen-type inequalities for a surface of constant curvature ⋮ The Bonnesen isoperimetric inequality in a surface of constant curvature ⋮ Some Bonnesen-style inequalities for higher dimensions ⋮ On containment measure and the mixed isoperimetric inequality ⋮ A kinematic formula for integral invariant of degree 4 in real space form ⋮ A sharp reverse Bonnesen-style inequality and generalization

Cites Work

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• The Willmore functional and the containment problem in \(R^{4}\)
• Blaschke's rolling theorem for manifolds with boundary
• The affine Sobolev inequality.
• Bonnesen-type inequalities for surfaces of constant curvature
• Normal and integral currents
• SOME NEW BONNESEN-STYLE INEQUALITIES
• Bonnesen-Style Isoperimetric Inequalities
• The isoperimetric inequality
• Geometric inequalities and inclusion measures of convex bodies
• On Willmore's Inequality for Submanifolds
• THE BONNESEN-TYPE INEQUALITIES IN A PLANE OF CONSTANT CURVATURE

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