The Bonnesen isoperimetric inequality in a surface of constant curvature

DOI10.1007/s11425-012-4405-zzbMath1260.52007OpenAlexW2045337044MaRDI QIDQ1933969

Lei Ma, Jia-zu Zhou, Fangwei Chen, Chunna Zeng

Publication date: 28 January 2013

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

Full work available at URL: https://doi.org/10.1007/s11425-012-4405-z

zbMATH Keywords

projective planehyperbolic planeconvex domainisoperimetric deficitkinematic formulaBonnesen isoperimetric inequality

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40) Convex sets in (2) dimensions (including convex curves) (52A10) Random convex sets and integral geometry (aspects of convex geometry) (52A22)

Related Items (15)

Bonnesen-style inequalities on surfaces of constant curvature ⋮ Translative containment measure and symmetric mixed isohomothetic inequalities ⋮ On Bonnesen-style symmetric mixed isohomothetic inequality in \(\mathbb{R}^2\) ⋮ Schur convex functions and the Bonnesen style isoperimetric inequalities for planar convex polygons ⋮ Reverse Bonnesen-style inequalities on surfaces of constant curvature ⋮ Bonnesen-style inequality for the first eigenvalue on a complete surface 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 ⋮ Unnamed Item ⋮ On containment measure and the mixed isoperimetric inequality ⋮ A kinematic formula for integral invariant of degree 4 in real space form ⋮ A new counterexample to Sangwine-Yager's conjecture ⋮ A sharp reverse Bonnesen-style inequality and generalization ⋮ A new integral formula for the angle between intersected submanifolds ⋮ Some Bonnesen-style Minkowski inequalities

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