Currents in snowflaked metric spaces
Currents in snowflaked metric spaces
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雪花状度量空间中的电流
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
Tobias Strubel
中科院分区：
文献类型：
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作者：
E. Donne;F. Polo;J. Portmann;L. Reichel;Christian Riedweg;Tobias Strubel
对于有向的n维Lipschitz流形M，当函数f，g1，. . .，gn仅仅是通过将RiemannStieltjes积分的构造扩展到更高的维度而具有一定阶的Hölder连续。更一般地，我们证明了对α ∈（nn +1，1]，局部紧度量空间（X，d）中的n维局部正规流表示（X，d）中的n维流的子空间.另一方面，当n ≥ 1且α ≤ nn +1时，（X，d）中n维流的向量空间为零。作为这些结果的一个特殊应用，证明了Hölder类α > 1 2的Heisenberg群中的曲面在xy平面上没有本质有界变分的投影.
For an oriented n-dimensional Lipschitz manifold M we give meaning to the integral ∫ M f dg1∧· · ·∧dgn in case the functions f, g1, . . . , gn are merely Hölder continuous of a certain order by extending the construction of the RiemannStieltjes integral to higher dimensions. More generally, we show that for α ∈ ( n n+1 , 1] the n-dimensional locally normal currents in a locally compact metric space (X, d) represent a subspace of the n-dimensional currents in (X, d). On the other hand, for n ≥ 1 and α ≤ n n+1 the vector space of n-dimensional currents in (X, d) is zero. As a particular application of these results it is shown that a surface in the Heisenberg group of Hölder class α > 1 2 does not have projection of essentially bounded varation onto the xy-plane.