• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.679-683
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• 1997

We obtain new upper bound of the area of a constant breath curve. We estimate the area of a constant breadth curve in terms of its breadth and minimal radius and the arc length of its pedal curve.

• Bulletin of the Korean Mathematical Society
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• v.36 no.1
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• pp.15-23
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• 1999

We obtain an efficient upper bound of the area of convex curves of constant relative breadth in the Minkowski plane. The estimation is given in terms of the Minkowski are length of pedal curve of original curve.

• Journal of the Korean Mathematical Society
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• v.48 no.4
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• pp.849-866
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• 2011

In this paper, we give the differential equations characterizing the timelike and spacelike curves of constant breadth in Minkowski 3-space $E^3_1$. Furthermore, we give a criterion for a timelike or spacelike curve to be the curve of constant breadth in $E^3_1$. As an example, the obtained results are applied to the case $\rho$ = const. and $k_2$ = const., and are discussed.