Singular sets of harmonic functions in R^2 and their complexifications in C^2
Singular sets of harmonic functions in R^2 and their complexifications in C^2
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R^2 中调和函数的奇异集及其在 C^2 中的复化
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
Qing Han
中科院分区：
文献类型：
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作者：
Qing Han
众所周知，b1∧r2中的（实）调和函数的临界集是孤立的。事实上，它们的全纯扩展的复临界集在c2中也是孤立的。证明了在0∈c2处的固定球的复临界集的个数以（实）单位球中调和函数频率的二次阶为界。
It is well known that the critical set of (real) harmonic functions in B 1 ⊂ R 2 is isolated. In fact, the complex critical set of their holomorphic extensions is also isolated in C 2 . It is shown that the number of complex critical set in a fixed ball at 0 ∈ C 2 is bounded by a quadratic order of the frequency of harmonic functions in the (real) unit ball.