For fixed w in (0, pi) excluding pi/2, the liminf and limsup of the infimal relative effective radius of constant-width bodies on S^n are bounded between positive explicit constants sigma_l(w) and sigma_u(w) both strictly less than 1.
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math.MG 2years
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The paper establishes optimal stability versions of the isominwidth inequality for ball convex bodies with respect to Hausdorff distance and symmetric difference metric in all three constant curvature planes.
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On the spherical Blaschke-Lebesgue problem
For fixed w in (0, pi) excluding pi/2, the liminf and limsup of the infimal relative effective radius of constant-width bodies on S^n are bounded between positive explicit constants sigma_l(w) and sigma_u(w) both strictly less than 1.
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Optimal stability of P\'al's isominwidth inequality for ball convex bodies in planes of constant curvature
The paper establishes optimal stability versions of the isominwidth inequality for ball convex bodies with respect to Hausdorff distance and symmetric difference metric in all three constant curvature planes.