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An application of valuation theory to two problems in discrete geometry

✍ Scribed by U. Betke; P. Gritzmann


Publisher
Elsevier Science
Year
1986
Tongue
English
Weight
303 KB
Volume
58
Category
Article
ISSN
0012-365X

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✦ Synopsis


First a new approach is given to the technique of simple valuations previously introduced by McMullen. Then, this method is used to establish some cases of Wills' conjecture on the number of lattice points in convex bodies and of L. Fejes T6th's sausage-conjecture on finite packings of the unit ball.


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The approach to oscillation theory developed by Gesztesy, Simon, and Teschl produces a sharp version for the oscillation theorem for singular Sturm-Liouville operators. In the present note, an example from the stability theory of complete minimal surfaces is given in which this refinement plays a de