| Abstract On Levels in Arrangements of Surfaces in Three Dimensions (2008) | |||||||||||||||
Abstract | |||||||||||||||
| A favorite open problem in combinatorial geonmtry is to determine the worst-case complexity of a level in an ar-rangement. Up to now, nontrivial upper bounds in three dimensions are known only for the linear cases of planes and triangles. We propose the first technique that can deal with more general surfaces in three dimensions. For example, in an arrangenmnt of n "pseudo-planes " or "pseudo-spheres" (where each triple of surfaces has at most two common inter-sections), we prove that there are at most O(n 299s6) vertices of any given level. | |||||||||||||||
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