A simple proof of an approximation theorem of H. Minkowski |
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Authors: | Michael Schmuckenschlaeger |
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Institution: | (1) Weizmann Institute of Science, 76100 Rehovot, Israel |
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Abstract: | It is proved that every convex bodyC inR
n
can be approximated by a sequenceC
k of convex bodies, whose boundary is the intersection of a level set of a homogeneous polynomial of degree 2k and a hyperplane. The Minkowski functional ofC
k is given explictly. Some further nice properties of the approximantsC
k are proved.Supported in part by BSF and Erwin Schrödinger Auslandsstipendium J0630. |
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Keywords: | |
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