On the sharpness of assumptions in the Federer theorem

IF 0.7 4区 数学 Q2 MATHEMATICS
B. Makarov, A. Podkorytov
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引用次数: 0

Abstract

The Federer theorem deals with the “massiveness” of the set of critical values for a t t -smooth map acting from R m \mathbb R^m to R n \mathbb R^n : it claims that the Hausdorff p p -measure of this set is zero for certain p p . If n m n\ge m , it has long been known that the assumption of that theorem relating the parameters m , n , t , p m,n,t,p is sharp. Here it is shown by an example that this assumption is also sharp for n > m n>m .

论费德勒定理中假设的尖锐性
费德勒定理处理的是从R m \mathbb R^m到R n \mathbb R^n的光滑映射的临界值集合的“海量性”:它声称该集合的Hausdorff p p -测度在特定的p p下为零。如果n≥m n\ge m,我们早就知道关于参数m,n,t,p m,n,t,p的定理的假设是尖锐的。这里的一个例子表明,这个假设对于n b>00 m和n bb11m也是尖锐的。
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来源期刊
CiteScore
1.00
自引率
12.50%
发文量
52
审稿时长
>12 weeks
期刊介绍: This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.
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