On Boundary Arcs Joining Antipodal Points of a Planar Convex Body
نویسنده
چکیده
Using notions of Minkowski geometry (i.e., of the geometry of finite dimensional Banach spaces) we find new characterizations of centrally symmetric convex bodies, equiframed curves, bodies of constant width and certain convex bodies with modified constant width property. In particular, we show that straightforward extensions of some properties of bodies of constant Euclidean width are also valid for bodies of constant Minkowskian width if the underlying Minkowskian circle is an equiframed curve. All obtained characterizations are restricted to the case of the plane and involve certain measures of boundary arcs that join antipodal points of a planar convex body. MSC 2000: 52A10, 52A38
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