Sufficient conditions for one domain to contain another in a space of constant curvature

DOI10.1090/S0002-9939-98-04369-XzbMath0918.53025MaRDI QIDQ4211009

Jia-zu Zhou

Publication date: 10 September 1998

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

mean curvatureconvex bodytotal geodesic curvatureGaussian curvaturekinematic formuladomaintransfer principleWeingarten transformation

Mathematics Subject Classification ID

Integral geometry (53C65) Inequalities and extremum problems in real or complex geometry (51M16) Random convex sets and integral geometry (aspects of convex geometry) (52A22)

Related Items (12)

Kinematic formulas of total mean curvatures for hypersurfaces ⋮ Bonnesen-type inequalities for surfaces of constant curvature ⋮ Reverse Bonnesen-style inequalities on surfaces of constant curvature ⋮ Reverse Bonnesen style inequalities in a surface \(\mathbb{X}_\epsilon ^2\) of constant curvature ⋮ The Willmore functional and the containment problem in \(R^{4}\) ⋮ Some Bonnesen-style inequalities for higher dimensions ⋮ Volume bounds for shadow covering ⋮ On containment measure and the mixed isoperimetric inequality ⋮ A kinematic formula for the total absolute curvature of intersections ⋮ Closed-form characterization of the Minkowski sum and difference of two ellipsoids ⋮ If you can hide behind it, can you hide inside it? ⋮ An integral formula for the total mean curvature matrix

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