Bulletin of the
Korean Mathematical Society BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016
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Bull. Korean Math. Soc. 1996; 33(4): 537-544

Printed December 1, 1996

Copyright © The Korean Mathematical Society.

A Crofton style formula and its application on the unit sphere

Y. D. Chai and Young Soo Lee

Sung Kyun Kwan University and Sung Kyun Kwan University

Abstract

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In this paper, we define strips on $S^2$ and their density and, using them, we obtain integral formulas which have relation to the strips. As an application of the formulas we develop some inequalities including area and perimeter of the closed convex curve on the unit sphere.

Keywords: Crofton's formula, strip, spherical curvature, parallel set, closed convex curve, maximum breadth

MSC numbers: 53C65, 52A10

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