Reconstruction of a plane convex body from the curvature of its boundary |
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Authors: | Michael Kallay |
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Institution: | (1) Department of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel |
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Abstract: | Let
denote the class of plane convex bodies having a width functionw, wherew′ is absolutely continuous. It is proved that a body in
is determined (up to translation) by the radius of curvature function of its boundary. This result is then used for a characterization
of the extreme (indecomposable) bodies in
and for a density theorem for Reuleaux polygons in
.
The content of this paper is a revised version of a part of the Master of Science thesis written by the author under the supervision
of Professor Micha A. Perles at the Hebrew University of Jerusalem and submitted in October, 1971. |
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Keywords: | |
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