Convergence of total variation of curvature measures
Convergence of total variation of curvature measures
复制标题
曲率测量总变差的收敛
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
J. Rataj
中科院分区：
文献类型：
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作者：
J. Rataj
摘要。已知当一个正达集或一个多凸集的平行邻域的曲率测度在其自身的曲率测度上趋于0时，其曲率测度模糊收敛。我们证明了在一个正伸展集的情况下，曲率测度的总变化也是收敛的，而在一个多凸集的情况下，这在一般情况下不再成立。
Abstract.It is known that the curvature measures of parallel ɛ-neighbourhoods of a set with positive reach or a polyconvex set converge vaguely if ɛ tends to zero to the curvature measures of the set itself. We show that in the case of a set with positive reach, the total variations of the curvature measures converge as well, whereas in the case of a polyconvex set this is no more true in general.