锋利的估计几何刚度第一海森堡组

Доклады Академии наук Pub Date : 2019-10-30 DOI:10.31857/s0869-56524886590-594

D. V. Isangulova

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引用次数: 0

摘要

我们用亚黎曼几何证明了第一Heisenberg群上等距的定量稳定性:Heisenberg群的John域的每一个(1 +)-拟等距在一致范数和Sobolev范数上都接近于某个接近阶的等距。最后给出了一个例子，证明了结果的渐近锐度。

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Sharp estimates of the geometric rigidity on the first Heisenberg group

We prove quantitative stability of isometries on the first Heisenberg group with sub-Riemannian geometry: every (1 + )-quasi-isometry of the John domain of the Heisenberg group is close to some isometry with order of closeness in the uniform norm and with the order of closeness+ in the Sobolev norm. An example demonstrating the asymptotic sharpness of the results is given.

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Доклады Академии наук

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