论文信息 - Bonnesen-type inequalities for surfaces of constant curvature

Bonnesen-type inequalities for surfaces of constant curvature

A Bonnesen-type inequality is a sharp isoperimetric inequality that includes an error estimate in terms of inscribed and circumscribed regions. A kinematic technique is used to prove a Bonnesen-type inequality for the Euclidean sphere (having constant Gauss curvature @k>0) and the hyperbolic plane (having constant Gauss curvature @k 0.

Daniel A. Klain

[1] Daniel A. Klain,et al. Introduction to Geometric Probability , 1997 .

[2] Dual kinematic formulas , 1999 .

[3] Jörg M. Wills,et al. Handbook of Convex Geometry , 1993 .

[4] T. Bonnesen. Über das isoperimetrische Defizit ebener Figuren , 1924 .

[5] L. Santaló. Integral geometry and geometric probability , 1976 .

[6] Robert Osserman,et al. BONNESEN-STYLE ISOPERIMETRIC INEQUALITIES , 1979 .

[7] K. Ball. CONVEX BODIES: THE BRUNN–MINKOWSKI THEORY , 1994 .

[8] Sufficient conditions for one domain to contain another in a space of constant curvature , 1998 .

[9] J. Stillwell. Geometry of surfaces , 1992 .

[10] H. hadwiger. Überdeckung ebener Bereiche durch Kreise und Quadrate , 1940 .

[11] R. Schneider,et al. CHAPTER 5.1 – Integral Geometry , 1993 .

[12] Ralph Howard,et al. The kinematic formula in Riemannian homogeneous spaces , 1993 .

[13] Daniel A. Klain. Isometry-Invariant Valuations on Hyperbolic Space , 2006, Discret. Comput. Geom..