Notes on Chern’s Affine Bernstein Conjecture
Notes on Chern’s Affine Bernstein Conjecture
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DOI：
10.1007/s00025-011-0182-1
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发表时间：
2011-04
影响因子：
2.2
通讯作者：
An-Min Li;Ruiwei Xu;U. Simon;F. Jia
中科院分区：
文献类型：
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作者：
An-Min Li;Ruiwei Xu;U. Simon;F. Jia
完备仿射极大曲面有两个著名的定理，一个是Calabi的，另一个是Chern的。大约十年前，通过研究相关的欧拉-拉格朗日方程，用不同的方法解决了这两个问题。本文综述了与陈省身仿射伯恩斯坦猜想有关的某些Monge-Ampère方程的研究中的最新进展和技术，特别是我们最近的专著（Li et al.在Affine伯恩斯坦问题和Monge-Ampère方程中，2010年）。此外，我们补充了一些细节的证明辅助材料，被遗漏的（李等。在Affine伯恩斯坦问题和Monge-Ampère方程中，2010年）。导言部分提供了相关的背景资料。
There were two famous conjectures oncomplete affine maximal surfaces, one due to Calabi, the other to Chern. Both were solved with different methods about one decade ago by studying the associated Euler-Lagrange equation. Here we survey recent developments and techniques in the study of certain Monge-Ampère equations associated withChern’s Affine Bernstein Conjecture, in particular two of its proofs in our recent monograph (Li et al. in Affine Bernstein problems and Monge-Ampère equations, 2010). In addition, we add some details of the proofs of auxiliary material that were omitted in (Li et al. in Affine Bernstein problems and Monge-Ampère equations, 2010). The related background information is provided in the Introduction.