紧致流形的全局Nash-Kuiper定理

IF 1.3 1区数学 Q1 MATHEMATICS

Journal of Differential Geometry Pub Date : 2019-06-20 DOI:10.4310/jdg/1668186787

Wentao Cao, L. Sz'ekelyhidi

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引用次数: 8

摘要

我们得到了具有最优Holder指数的紧致流形的$C^｛1，θ｝$等距浸入的著名Nash-Kuiper定理的全局扩展。特别是对于在3空间中等距嵌入凸紧致表面的Weyl问题，我们证明了Nash-Kuiper非刚性在指数$\theta<1/5$之前占主导地位。这扩展了先前关于嵌入2-二元以及更高维类似物的结果。

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Global Nash–Kuiper theorem for compact manifolds

We obtain global extensions of the celebrated Nash-Kuiper theorem for $C^{1,\theta}$ isometric immersions of compact manifolds with optimal Holder exponent. In particular for the Weyl problem of isometrically embedding a convex compact surface in 3-space, we show that the Nash-Kuiper non-rigidity prevails upto exponent $\theta<1/5$. This extends previous results on embedding 2-discs as well as higher dimensional analogues.

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来源期刊

Journal of Differential Geometry 数学-数学

CiteScore

3.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Publishes the latest research in differential geometry and related areas of differential equations, mathematical physics, algebraic geometry, and geometric topology.