Volumes of tubular neighbourhoods of real algebraic varieties.
Volumes of tubular neighbourhoods of real algebraic varieties.
复制标题
实代数簇的管状邻域体积。
DOI：
10.2140/pjm.1993.159.177
复制
发表时间：
1993
影响因子：
0.6
通讯作者：
Richard Wongkew
中科院分区：
文献类型：
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作者：
Richard Wongkew
本文讨论了以下问题：设V是^维欧氏空间中的代数簇。对于每一对正数p和R，求出该组点的体积的一个上界，该点集距离V在p的距离内，并且在距离固定点po的距离R内。得到这个上界，这样它就与po的选择无关。具体地说，是否存在通用的w次多项式，例如Pπ(，，·)，它在输入p，R和V的次数时自动提供上界？
This paper concerns the following problem: Let V be an algebraic variety in ^-dimensional euclidean space. For each pair of positive numbers p and R find an upper bound on the volume of the set of points that are within a distance of p from V and within a distance R from a fixed point po . Obtain this upper bound so that it is independent of the choice of po . In particular, does there exist a universal wth-degree polynomial, say P π ( , , •) which automatically provides an upper bound upon entering p , R and the degree of V ?