COMPLEXITY RESULTS FOR CR MAPPINGS BETWEEN SPHERES
COMPLEXITY RESULTS FOR CR MAPPINGS BETWEEN SPHERES
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DOI：
10.1142/s0129167x09005248
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发表时间：
2007-08
影响因子：
0.6
通讯作者：
J. D'Angelo;Jiří Lebl
中科院分区：
文献类型：
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作者：
J. D'Angelo;Jiří Lebl
使用初等数论，我们证明了关于球体之间 CR 映射复杂性的几个结果。众所周知，球体之间的 CR 映射在有限群下不变，导致超平面上实多项式常数的度估计出现尖锐界限。我们在这里表明，尖锐例子的唯一性在无数程度上都失效了。证明使用佩尔方程。然后我们锐化我们的结果并获得保证非唯一性的各种同余性。我们还表明，球之间正确映射的间隙现象不会在超出特定目标尺寸时发生。这个证明使用了邮票问题的解决方案。
Using elementary number theory, we prove several results about the complexity of CR mappings between spheres. It is known that CR mappings between spheres, invariant under finite groups, lead to sharp bounds for degree estimates on real polynomials constant on a hyperplane. We show here that there are infinitely many degrees for which the uniqueness of sharp examples fails. The proof uses a Pell equation. We then sharpen our results and obtain various congruences guaranteeing nonuniqueness. We also show that a gap phenomenon for proper mappings between balls does not occur beyond a certain target dimension. This proof uses the solution of the postage stamp problem.